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Journal articles on the topic 'Combinatorial statistics'

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Author: Grafiati

Published: 20 July 2024

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1

Gerards, A. M. H., and A. W. J. Kolen. "Polyhedral Combinatorics in Combinatorial Optimization." Statistica Neerlandica 41, no. 1 (March 1987): 1–25. http://dx.doi.org/10.1111/j.1467-9574.1987.tb01168.x.

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2

Niven, R. K. "Combinatorial entropies and statistics." European Physical Journal B 70, no. 1 (May 16, 2009): 49–63. http://dx.doi.org/10.1140/epjb/e2009-00168-5.

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3

Hansen, J. C. "Order statistics for random combinatorial structures." Advances in Applied Probability 24, no. 4 (December 1992): 774. http://dx.doi.org/10.1017/s0001867800024836.

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4

Denise, Alain, and Rodica Simion. "Two combinatorial statistics on Dyck paths." Discrete Mathematics 137, no. 1-3 (January 1995): 155–76. http://dx.doi.org/10.1016/0012-365x(93)e0147-v.

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5

Simion, Rodica. "Combinatorial statistics on non-crossing partitions." Journal of Combinatorial Theory, Series A 66, no. 2 (May 1994): 270–301. http://dx.doi.org/10.1016/0097-3165(94)90066-3.

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6

Hansen, Jennie C. "Order statistics for decomposable combinatorial structures." Random Structures & Algorithms 5, no. 4 (October 1994): 517–33. http://dx.doi.org/10.1002/rsa.3240050404.

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7

Calvin, James A., and Marshall Hall. "Combinatorial Theory." Journal of the American Statistical Association 82, no. 400 (December 1987): 1197. http://dx.doi.org/10.2307/2289431.

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8

Bernabei, Maria Simonetta, and Horst Thaler. "Central Limit Theorem for Coloured Hard Dimers." Journal of Probability and Statistics 2010 (2010): 1–13. http://dx.doi.org/10.1155/2010/781681.

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We study the central limit theorem for a class of coloured graphs. This means that we investigate the limit behavior of certain random variables whose values are combinatorial parameters associated to these graphs. The techniques used at arriving this result comprise combinatorics, generating functions, and conditional expectations.

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9

SCHORK, MATTHIAS. "SOME ALGEBRAICAL, COMBINATORIAL AND ANALYTICAL PROPERTIES OF PARAGRASSMANN VARIABLES." International Journal of Modern Physics A 20, no. 20n21 (August 20, 2005): 4797–819. http://dx.doi.org/10.1142/s0217751x05025127.

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Some algebraical, combinatorial and analytical aspects of paragrassmann variables are discussed. In particular, the similarity of the combinatorics involved with those of generalized exclusion statistics (Gentile's intermediate statistics) is stressed. It is shown that the dimensions of the algebras of generalized grassmann variables are related to generalized Fibonacci numbers. On the analytical side, some of the simplest differential equations are discussed and a suitably generalized Berezin integral as well as an associated delta-function are considered. Some remarks concerning a geometrical interpretation of recent results about fractional superconformal transformations involving generalized grassmann variables are given. Finally, a quantity related to the Witten index is discussed.

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10

Crane, Harry. "Combinatorial Lévy processes." Annals of Applied Probability 28, no. 1 (February 2018): 285–339. http://dx.doi.org/10.1214/17-aap1306.

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11

SHEVCHENKO, VLADIMIR. "INFINITE STATISTICS, SYMMETRY BREAKING AND COMBINATORIAL HIERARCHY." Modern Physics Letters A 24, no. 18 (June 14, 2009): 1425–35. http://dx.doi.org/10.1142/s0217732309030825.

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The physics of symmetry breaking in theories with strongly interacting quanta obeying infinite (quantum Boltzmann) statistics known as quons is discussed. The picture of Bose/Fermi particles as low energy excitations over nontrivial quon condensate is advocated. Using induced gravity arguments, it is demonstrated that the Planck mass in such low energy effective theory can be factorially (in number of degrees of freedom) larger than its true ultraviolet cutoff. Thus, the assumption that statistics of relevant high energy excitations is neither Bose nor Fermi but infinite can remove the hierarchy problem without necessity to introduce any artificially large numbers. Quantum mechanical model illustrating this scenario is presented.

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12

Vellaisamy, Palaniappan, and Aklilu Zeleke. "Exponential order statistics and some combinatorial identities." Communications in Statistics - Theory and Methods 48, no. 20 (October 29, 2018): 5099–105. http://dx.doi.org/10.1080/03610926.2018.1508710.

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13

Dean, Angela, and Gregory M. Constantine. "Combinatorial Theory and Statistical Design." Journal of the American Statistical Association 84, no. 408 (December 1989): 1103. http://dx.doi.org/10.2307/2290108.

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14

Tierney, Luke, R. C. Bose, B. Manvel, Fred S. Roberts, and Kenneth P. Bogart. "Introduction to Combinatorial Theory." Journal of the American Statistical Association 80, no. 389 (March 1985): 246. http://dx.doi.org/10.2307/2288096.

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15

Bombelli, L., A. Corichi, and O. Winkler. "Semiclassical quantum gravity: statistics of combinatorial Riemannian geometries." Annalen der Physik 517, no. 8 (July 12, 2005): 499–519. http://dx.doi.org/10.1002/andp.20055170803.

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16

Bombelli, L., A. Corichi, and O. Winkler. "Semiclassical quantum gravity: statistics of combinatorial Riemannian geometries." Annalen der Physik 14, no. 8 (August 1, 2005): 499–519. http://dx.doi.org/10.1002/andp.200410144.

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17

Ibrahim, M., and A. Musa. "A Study of Some New Statistics on the - non-Deranged Permutations." International Journal of Science for Global Sustainability 9, no. 1 (March 31, 2023): 6. http://dx.doi.org/10.57233/ijsgs.v9i1.406.

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In this study, we looked at some novel statistics on the -non deranged permutation group, a symmetric group subgroup. We analyzed and redefined some of the statistic namely Lmap, Lmal, Rmip, Rmil and Rmal on -non deranged permutations. We found that in all -non deranged permutations, Lmap is equivalent to Lmal. In addition, we observed that Rmal of is empty for any and other combinatorial features.

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18

Avila, Artur, Jeremy Kahn, Mikhail Lyubich, and Weixiao Shen. "Combinatorial rigidity for unicritical polynomials." Annals of Mathematics 170, no. 2 (September 1, 2009): 783–97. http://dx.doi.org/10.4007/annals.2009.170.783.

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19

Neykov, Matey, Junwei Lu, and Han Liu. "Combinatorial inference for graphical models." Annals of Statistics 47, no. 2 (April 2019): 795–827. http://dx.doi.org/10.1214/17-aos1650.

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20

Lykke Jacobsen, Jesper, and Hubert Saleur. "Combinatorial aspects of boundary loop models." Journal of Statistical Mechanics: Theory and Experiment 2008, no. 01 (January 29, 2008): P01021. http://dx.doi.org/10.1088/1742-5468/2008/01/p01021.

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21

Marschner, Ian C. "Combinatorial EM algorithms." Statistics and Computing 24, no. 6 (July 19, 2013): 921–40. http://dx.doi.org/10.1007/s11222-013-9411-7.

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22

Volovik, A. V. "A combinatorial method of small sample identification." Dependability 24, no. 2 (May 21, 2024): 3–7. http://dx.doi.org/10.21683/1729-2646-2024-24-2-3-7.

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Aim. For the purpose of improving the reliability of decisions regarding the uniformity of distributions over samples of limited size, a combinatorial method has been developed for defining a criterion based on simple combinations of sample values. Methods. The paper uses methods of the probability theory, mathematical statistics, and combinatorics. Results. The proposed criterion is highly efficient for distinguishing small samples when testing statistically similar hypotheses, such as the hypothesis of a uniform distribution law and the hypothesis of a beta distribution of the first kind. Conclusions. The approach proposed in the paper enables a sequential analysis procedure (detection of process “imbalance”). This procedure makes it possible to reliably detect the “imbalance” (deviation of the distribution of observations from the uniform law) of a process with a practically sufficient intensity using recurrent relations.

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23

Gnedin, Alexander V. "Regeneration in random combinatorial structures." Probability Surveys 7 (2010): 105–56. http://dx.doi.org/10.1214/10-ps163.

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24

Albrecher, Hansjörg, Jozef Teugels, and Klaus Scheicher. "A combinatorial identity for a problem in asymptotic statistics." Applicable Analysis and Discrete Mathematics 3, no. 1 (2009): 64–68. http://dx.doi.org/10.2298/aadm0901064a.

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Let (Xi)i?1 be a sequence of positive independent identically distributed random variables with regularly varying distribution tail of index 0 < ? < 1 and define Tn = X1?+X2?+???+Xn?/(X1+X2+???+ Xn)?.In this note we simplify an expression for lim n?? E(T kn ), which was obtained by Albrecher and Teugels: Asymptotic analysis of a measure of variation. Theory Prob. Math. Stat., 74 (2006), 1-9, in terms of coefficients of a continued fraction expansion. The new formula establishes an unexpected link to an enumeration problem for rooted maps on orientable surfaces that was studied in Arqu?s and B?raud: Rooted maps of orientable surfaces, Riccati's equation and continued fractions. Discrete Mathematics, 215 (2000), 1-12.

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25

Mason, David M., and Tatyana S. Turova. "Motoo's combinatorial central limit theorem for serial rank statistics." Journal of Statistical Planning and Inference 91, no. 2 (December 2000): 427–40. http://dx.doi.org/10.1016/s0378-3758(00)00192-0.

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26

Eriksson, Kimmo. "Statistical and Combinatorial Aspects of Comparative Genomics*." Scandinavian Journal of Statistics 31, no. 2 (June 2004): 203–16. http://dx.doi.org/10.1111/j.1467-9469.2004.02-114.x.

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27

Demange, Gabrielle, and Xiaotie Deng. "Universally Balanced Combinatorial Optimization Games." Games 1, no. 3 (September 13, 2010): 299–316. http://dx.doi.org/10.3390/g1030299.

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28

Benjamin, Arthur T., Larry Ericksen, Pallavi Jayawant, and Mark Shattuck. "Combinatorial trigonometry with Chebyshev polynomials." Journal of Statistical Planning and Inference 140, no. 8 (August 2010): 2157–60. http://dx.doi.org/10.1016/j.jspi.2010.01.011.

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29

RVL, Charles J. Colbourne, and Jeffrey H. Dinitz. "The CRC Handbook of Combinatorial Designs." Journal of the American Statistical Association 92, no. 438 (June 1997): 800. http://dx.doi.org/10.2307/2965756.

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30

Indlekofer, Karl-Heinz. "On Labeled and Unlabeled Combinatorial Structures." Communications in Statistics - Theory and Methods 40, no. 19-20 (October 2011): 3641–53. http://dx.doi.org/10.1080/03610926.2011.581184.

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31

Ramamurthy, K. G., Arvind Seth, and Mohammad Khanjari Sadegh. "A Combinatorial Approach for Component Importance." Communications in Statistics - Theory and Methods 32, no. 2 (January 3, 2003): 497–507. http://dx.doi.org/10.1081/sta-120018197.

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32

Hyde, Trevor. "Polynomial Factorization Statistics and Point Configurations in ℝ3." International Mathematics Research Notices 2020, no. 24 (December 11, 2018): 10154–79. http://dx.doi.org/10.1093/imrn/rny271.

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Abstract We use combinatorial methods to relate the expected values of polynomial factorization statistics over $\mathbb{F}_q$ to the cohomology of ordered configurations in $\mathbb{R}^3$ as a representation of the symmetric group. Our method gives a new proof of the twisted Grothendieck–Lefschetz formula for squarefree polynomial factorization statistics of Church, Ellenberg, and Farb.

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33

Balasubramanian, Krishnan. "Symmetry, Combinatorics, Artificial Intelligence, Music and Spectroscopy." Symmetry 13, no. 10 (October 2, 2021): 1850. http://dx.doi.org/10.3390/sym13101850.

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Symmetry forms the foundation of combinatorial theories and algorithms of enumeration such as Möbius inversion, Euler totient functions, and the celebrated Pólya’s theory of enumeration under the symmetric group action. As machine learning and artificial intelligence techniques play increasingly important roles in the machine perception of music to image processing that are central to many disciplines, combinatorics, graph theory, and symmetry act as powerful bridges to the developments of algorithms for such varied applications. In this review, we bring together the confluence of music theory and spectroscopy as two primary disciplines to outline several interconnections of combinatorial and symmetry techniques in the development of algorithms for machine generation of musical patterns of the east and west and a variety of spectroscopic signatures of molecules. Combinatorial techniques in conjunction with group theory can be harnessed to generate the musical scales, intensity patterns in ESR spectra, multiple quantum NMR spectra, nuclear spin statistics of both fermions and bosons, colorings of hyperplanes of hypercubes, enumeration of chiral isomers, and vibrational modes of complex systems including supergiant fullerenes, as exemplified by our work on the golden fullerene C150,000. Combinatorial techniques are shown to yield algorithms for the enumeration and construction of musical chords and scales called ragas in music theory, as we exemplify by the machine construction of ragas and machine perception of musical patterns. We also outline the applications of Hadamard matrices and magic squares in the development of algorithms for the generation of balanced-pitch chords. Machine perception of musical, spectroscopic, and symmetry patterns are considered.

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34

Frolov, Andrei N. "On combinatorial strong law of large numbers and rank statistics." Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy 65, no. 3 (2020): 490–99. http://dx.doi.org/10.21638/spbu01.2020.311.

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35

Frolov, A. N. "On Combinatorial Strong Law of Large Numbers and Rank Statistics." Vestnik St. Petersburg University, Mathematics 53, no. 3 (July 2020): 336–43. http://dx.doi.org/10.1134/s1063454120030073.

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36

KAMEOKA, Koichi, Makoto NAKATANI, and Norio INUI. "Phenomena in Probability and Statistics Found in a Combinatorial Weigher." Transactions of the Society of Instrument and Control Engineers 36, no. 5 (2000): 388–94. http://dx.doi.org/10.9746/sicetr1965.36.388.

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37

Rawlings, D. P., and N. Balakrishnan. "Advances in Combinatorial Methods and Applications to Probability and Statistics." Biometrics 54, no. 4 (December 1998): 1681. http://dx.doi.org/10.2307/2533700.

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38

MTW and N. Balakrishnan. "Advances in Combinatorial Methods and Applications to Probability and Statistics." Journal of the American Statistical Association 93, no. 443 (September 1998): 1251. http://dx.doi.org/10.2307/2669904.

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39

LUNDY, M. "Applications of the annealing algorithm to combinatorial problems in statistics." Biometrika 72, no. 1 (1985): 191–98. http://dx.doi.org/10.1093/biomet/72.1.191.

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40

徐, 晨. "Proofs of Several Combinatorial Identities Based on Probability Statistics Method." Advances in Applied Mathematics 13, no. 01 (2024): 127–32. http://dx.doi.org/10.12677/aam.2024.131015.

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41

Manolescu, Ciprian, Peter Ozsváth, and Sucharit Sarkar. "A combinatorial description of knot Floer homology." Annals of Mathematics 169, no. 2 (March 1, 2009): 633–60. http://dx.doi.org/10.4007/annals.2009.169.633.

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42

Aardal, K., and C. P. M. Hoesel. "Polyhedral techniques in combinatorial optimization I: Theory." Statistica Neerlandica 50, no. 1 (March 1996): 3–26. http://dx.doi.org/10.1111/j.1467-9574.1996.tb01478.x.

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43

Frolov, Andrei N. "On large deviations for combinatorial sums." Journal of Statistical Planning and Inference 217 (March 2022): 24–32. http://dx.doi.org/10.1016/j.jspi.2021.07.002.

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44

Chatterjee, Sourav, and Soumik Pal. "A Combinatorial Analysis of Interacting Diffusions." Journal of Theoretical Probability 24, no. 4 (December 31, 2009): 939–68. http://dx.doi.org/10.1007/s10959-009-0269-8.

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45

Coja-Oghlan, Amin, Tobias Kapetanopoulos, and Noela Müller. "The replica symmetric phase of random constraint satisfaction problems." Combinatorics, Probability and Computing 29, no. 3 (December 3, 2019): 346–422. http://dx.doi.org/10.1017/s0963548319000440.

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AbstarctRandom constraint satisfaction problems play an important role in computer science and combinatorics. For example, they provide challenging benchmark examples for algorithms, and they have been harnessed in probabilistic constructions of combinatorial structures with peculiar features. In an important contribution (Krzakala et al. 2007, Proc. Nat. Acad. Sci.), physicists made several predictions on the precise location and nature of phase transitions in random constraint satisfaction problems. Specifically, they predicted that their satisfiability thresholds are quite generally preceded by several other thresholds that have a substantial impact both combinatorially and computationally. These include the condensation phase transition, where long-range correlations between variables emerge, and the reconstruction threshold. In this paper we prove these physics predictions for a broad class of random constraint satisfaction problems. Additionally, we obtain contiguity results that have implications for Bayesian inference tasks, a subject that has received a great deal of interest recently (e.g. Banks et al. 2016, Proc. 29th COLT).

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46

BRINGMANN, KATHRIN, KARL MAHLBURG, and ROBERT C. RHOADES. "Taylor coefficients of mock-Jacobi forms and moments of partition statistics." Mathematical Proceedings of the Cambridge Philosophical Society 157, no. 2 (July 9, 2014): 231–51. http://dx.doi.org/10.1017/s0305004114000292.

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AbstractWe develop a new technique for deriving asymptotic series expansions for moments of combinatorial generating functions that uses the transformation theory of Jacobi forms and “mock” Jacobi forms, as well as the Hardy-Ramanujan Circle Method. The approach builds on a suggestion of Zagier, who observed that the moments of a combinatorial statistic can be simultaneously encoded as the Taylor coefficients of a function that transforms as a Jacobi form. Our use of Jacobi transformations is a novel development in the subject, as previous results on the asymptotic behavior of the Taylor coefficients of Jacobi forms have involved the study of each such coefficient individually using the theory of quasimodular forms and quasimock modular forms.As an application, we find asymptotic series for the moments of the partition rank and crank statistics. Although the coefficients are exponentially large, the error in the series expansions is polynomial, and have the same order as the coefficients of the residual Eisenstein series that are undetectable by the Circle Method. We also prove asymptotic series expansions for the symmetrized rank and crank moments introduced by Andrews and Garvan, respectively. Equivalently, the former gives asymptotic series for the enumeration of Andrews k-marked Durfee symbols.

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47

Shattuck, Mark. "Generalizations of Bell number formulas of spivey and Mező." Filomat 30, no. 10 (2016): 2683–94. http://dx.doi.org/10.2298/fil1610683s.

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We provide q-generalizations of Spivey?s Bell number formula in various settings by considering statistics on different combinatorial structures. This leads to new identities involving q-Stirling numbers of both kinds and q-Lah numbers. As corollaries, we obtain identities for both binomial and q-binomial coefficients. Our results at the same time also generalize recent r-Stirling number formulas of Mez?. Finally, we provide a combinatorial proof and refinement of Xu?s extension of Spivey?s formula to the generalized Stirling numbers of Hsu and Shiue. To do so, we develop a combinatorial interpretation for these numbers in terms of extended Lah distributions.

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48

Gamalo, Margaret. "Networked knowledge, combinatorial creativity, and (statistical) innovation." Journal of Biopharmaceutical Statistics 31, no. 2 (March 4, 2021): 109–12. http://dx.doi.org/10.1080/10543406.2021.1907889.

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49

Harrison, J. M., J. P. Keating, and J. M. Robbins. "Quantum statistics on graphs." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 467, no. 2125 (July 21, 2010): 212–33. http://dx.doi.org/10.1098/rspa.2010.0254.

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Quantum graphs are commonly used as models of complex quantum systems, for example molecules, networks of wires and states of condensed matter. We consider quantum statistics for indistinguishable spinless particles on a graph, concentrating on the simplest case of Abelian statistics for two particles. In spite of the fact that graphs are locally one dimensional, anyon statistics emerge in a generalized form. A given graph may support a family of independent anyon phases associated with topologically inequivalent exchange processes. In addition, for sufficiently complex graphs, there appear new discrete-valued phases. Our analysis is simplified by considering combinatorial rather than metric graphs—equivalently, a many-particle tight-binding model. The results demonstrate that graphs provide an arena in which to study new manifestations of quantum statistics. Possible applications include topological quantum computing, topological insulators, the fractional quantum Hall effect, superconductivity and molecular physics.

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50

Williams, Christopher K. I., and Michalis K. Titsias. "Greedy Learning of Multiple Objects in Images Using Robust Statistics and Factorial Learning." Neural Computation 16, no. 5 (May 1, 2004): 1039–62. http://dx.doi.org/10.1162/089976604773135096.

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We consider data that are images containing views of multiple objects. Our task is to learn about each of the objects present in the images. This task can be approached as a factorial learning problem, where each image must be explained by instantiating a model for each of the objects present with the correct instantiation parameters. A major problem with learning a factorial model is that as the number of objects increases, there is a combinatorial explosion of the number of configurations that need to be considered. We develop a method to extract object models sequentially from the data by making use of a robust statistical method, thus avoiding the combinatorial explosion, and present results showing successful extraction of objects from real images.

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