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Artykuły w czasopismach na temat „Lattices and Combinatorics”

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Autor: Grafiati

Data publikacji: 4 czerwca 2021

Data aktualizacji: 28 stycznia 2023

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1

Mühle, Henri. "Noncrossing Arc Diagrams, Tamari Lattices, and Parabolic Quotients of the Symmetric Group". Annals of Combinatorics 25, nr 2 (10.04.2021): 307–44. http://dx.doi.org/10.1007/s00026-021-00532-9.

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AbstractOrdering permutations by containment of inversion sets yields a fascinating partial order on the symmetric group: the weak order. This partial order is, among other things, a semidistributive lattice. As a consequence, every permutation has a canonical representation as a join of other permutations. Combinatorially, these canonical join representations can be modeled in terms of arc diagrams. Moreover, these arc diagrams also serve as a model to understand quotient lattices of the weak order. A particularly well-behaved quotient lattice of the weak order is the well-known Tamari lattice, which appears in many seemingly unrelated areas of mathematics. The arc diagrams representing the members of the Tamari lattices are better known as noncrossing partitions. Recently, the Tamari lattices were generalized to parabolic quotients of the symmetric group. In this article, we undertake a structural investigation of these parabolic Tamari lattices, and explain how modified arc diagrams aid the understanding of these lattices.

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2

Clingher, Adrian, i Jae-Hyouk Lee. "Lorentzian Lattices and E-Polytopes". Symmetry 10, nr 10 (28.09.2018): 443. http://dx.doi.org/10.3390/sym10100443.

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We consider certain E n -type root lattices embedded within the standard Lorentzian lattice Z n + 1 ( 3 ≤ n ≤ 8 ) and study their discrete geometry from the point of view of del Pezzo surface geometry. The lattice Z n + 1 decomposes as a disjoint union of affine hyperplanes which satisfy a certain periodicity. We introduce the notions of line vectors, rational conic vectors, and rational cubics vectors and their relations to E-polytopes. We also discuss the relation between these special vectors and the combinatorics of the Gosset polytopes of type ( n − 4 ) 21 .

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3

Mühle, Henri. "Hochschild lattices and shuffle lattices". European Journal of Combinatorics 103 (czerwiec 2022): 103521. http://dx.doi.org/10.1016/j.ejc.2022.103521.

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4

Baranovskii, Evgenii, i Viatcheslav Grishukhin. "Non-rigidity Degree of a Lattice and Rigid Lattices". European Journal of Combinatorics 22, nr 7 (październik 2001): 921–35. http://dx.doi.org/10.1006/eujc.2001.0510.

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5

Cuntz, Michael, Sophia Elia i Jean-Philippe Labbé. "Congruence Normality of Simplicial Hyperplane Arrangements via Oriented Matroids". Annals of Combinatorics 26, nr 1 (8.11.2021): 1–85. http://dx.doi.org/10.1007/s00026-021-00555-2.

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AbstractA catalogue of simplicial hyperplane arrangements was first given by Grünbaum in 1971. These arrangements naturally generalize finite Coxeter arrangements and also the weak order through the poset of regions. The weak order is known to be a congruence normal lattice, and congruence normality of lattices of regions of simplicial arrangements can be determined using polyhedral cones called shards. In this article, we update Grünbaum’s catalogue by providing normals realizing all known simplicial arrangements with up to 37 lines and key invariants. Then we add structure to this catalogue by determining which arrangements always/sometimes/never lead to congruence normal lattices of regions. To this end, we use oriented matroids to recast shards as covectors to determine congruence normality of large hyperplane arrangements. We also show that lattices of regions coming from finite Weyl groupoids of any rank are always congruence normal.

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6

Elekes, György. "On Linear Combinatorics III. Few Directions and Distorted Lattices". Combinatorica 19, nr 1 (1.01.1999): 43–53. http://dx.doi.org/10.1007/s004930050044.

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7

Vaderlind, Paul. "Clutters and Atomistic Lattices". European Journal of Combinatorics 7, nr 4 (październik 1986): 389–96. http://dx.doi.org/10.1016/s0195-6698(86)80010-5.

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8

Nimbhorkar, Shriram K., i Deepali B. Banswal. "Generalizations of supplemented lattices". AKCE International Journal of Graphs and Combinatorics 16, nr 1 (1.04.2019): 8–17. http://dx.doi.org/10.1016/j.akcej.2018.02.005.

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9

Leoreanu-Fotea, Violeta, i Ivo G. Rosenberg. "Hypergroupoids determined by lattices". European Journal of Combinatorics 31, nr 3 (kwiecień 2010): 925–31. http://dx.doi.org/10.1016/j.ejc.2009.06.005.

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10

Deza, Antoine, i Shmuel Onn. "Solitaire Lattices". Graphs and Combinatorics 18, nr 2 (1.05.2002): 227–43. http://dx.doi.org/10.1007/s003730200016.

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11

Stanley, Richard P. "Further Combinatorial Properties of Two Fibonacci Lattices". European Journal of Combinatorics 11, nr 2 (marzec 1990): 181–88. http://dx.doi.org/10.1016/s0195-6698(13)80072-8.

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12

Wild, Marcel. "Cover preserving embedding of modular lattices into partition lattices". Discrete Mathematics 112, nr 1-3 (marzec 1993): 207–44. http://dx.doi.org/10.1016/0012-365x(93)90235-l.

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13

Lefmann, Hanno. "On Families in Finite Lattices". European Journal of Combinatorics 11, nr 2 (marzec 1990): 165–79. http://dx.doi.org/10.1016/s0195-6698(13)80071-6.

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14

Li, Huiling. "On Basis-transitive Geometric Lattices". European Journal of Combinatorics 10, nr 6 (listopad 1989): 561–73. http://dx.doi.org/10.1016/s0195-6698(89)80073-3.

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15

Klain, Daniel A. "Kinematic formulas for finite lattices". Annals of Combinatorics 1, nr 1 (grudzień 1997): 353–66. http://dx.doi.org/10.1007/bf02558486.

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16

Chapman, Robin. "Steinitz classes of unimodular lattices". European Journal of Combinatorics 25, nr 4 (maj 2004): 487–93. http://dx.doi.org/10.1016/j.ejc.2003.02.001.

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17

McMullen, Peter. "Lattices compatible with regular polytopes". European Journal of Combinatorics 29, nr 8 (listopad 2008): 1925–32. http://dx.doi.org/10.1016/j.ejc.2008.01.005.

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18

Maehara, H. "Planar lattices and equilateral polygons". European Journal of Combinatorics 80 (sierpień 2019): 277–86. http://dx.doi.org/10.1016/j.ejc.2018.02.015.

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19

Deza, M., i V. P. Grishukhin. "Cut Lattices and Equiangular Lines". European Journal of Combinatorics 17, nr 2-3 (luty 1996): 143–56. http://dx.doi.org/10.1006/eujc.1996.0013.

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20

Chapman, Robin. "Conference Matrices and Unimodular Lattices". European Journal of Combinatorics 22, nr 8 (listopad 2001): 1033–45. http://dx.doi.org/10.1006/eujc.2001.0539.

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21

Brenti, Francesco. "Log-concavity and Combinatorial Properties of Fibonacci Lattices". European Journal of Combinatorics 12, nr 6 (listopad 1991): 459–76. http://dx.doi.org/10.1016/s0195-6698(13)80097-2.

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22

Harada, Masaaki, i Masaaki Kitazume. "Z4-Code Constructions for the Niemeier Lattices and their Embeddings in the Leech Lattice". European Journal of Combinatorics 21, nr 4 (maj 2000): 473–85. http://dx.doi.org/10.1006/eujc.1999.0360.

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23

Gaborit, Philippe. "Construction of new extremal unimodular lattices". European Journal of Combinatorics 25, nr 4 (maj 2004): 549–64. http://dx.doi.org/10.1016/j.ejc.2003.07.005.

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24

Šunić, Zoran. "Tamari lattices, forests and Thompson monoids". European Journal of Combinatorics 28, nr 4 (maj 2007): 1216–38. http://dx.doi.org/10.1016/j.ejc.2006.02.001.

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25

Wang, Kaishun, i Zengti Li. "Lattices associated with distance-regular graphs". European Journal of Combinatorics 29, nr 2 (luty 2008): 379–85. http://dx.doi.org/10.1016/j.ejc.2007.02.008.

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26

Felsner, Stefan, i Kolja Knauer. "Distributive lattices, polyhedra, and generalized flows". European Journal of Combinatorics 32, nr 1 (styczeń 2011): 45–59. http://dx.doi.org/10.1016/j.ejc.2010.07.011.

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27

Regonati, Francesco. "Upper Semimodularity of Finite Subgroup Lattices". European Journal of Combinatorics 17, nr 4 (maj 1996): 409–20. http://dx.doi.org/10.1006/eujc.1996.0034.

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28

Aramova, Annetta, Jürgen Herzog i Takayuki Hibi. "Finite Lattices and Lexicographic Gröbner Bases". European Journal of Combinatorics 21, nr 4 (maj 2000): 431–39. http://dx.doi.org/10.1006/eujc.1999.0358.

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29

Borovik, Alexandre V., Israel M. Gelfand i Neil White. "Representations of Matroids in Semimodular Lattices". European Journal of Combinatorics 22, nr 6 (sierpień 2001): 789–99. http://dx.doi.org/10.1006/eujc.2001.0504.

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30

Méndez, Miguel A., i José L. Ramírez. "A new approach to the r-Whitney numbers by using combinatorial differential calculus". Acta Universitatis Sapientiae, Mathematica 11, nr 2 (1.12.2019): 387–418. http://dx.doi.org/10.2478/ausm-2019-0029.

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Abstract In the present article we introduce two new combinatorial interpretations of the r-Whitney numbers of the second kind obtained from the combinatorics of the differential operators associated to the grammar G := {y → yxm, x → x}. By specializing m = 1 we obtain also a new combinatorial interpretation of the r-Stirling numbers of the second kind. Again, by specializing to the case r = 0 we introduce a new generalization of the Stirling number of the second kind and through them a binomial type family of polynomials that generalizes Touchard’s polynomials. Moreover, we recover several known identities involving the r-Dowling polynomials and the r-Whitney numbers using the combinatorial differential calculus. We construct a family of posets that generalize the classical Dowling lattices. The r-Withney numbers of the first kind are obtained as the sum of the Möbius function over elements of a given rank. Finally, we prove that the r-Dowling polynomials are a Sheffer family relative to the generalized Touchard binomial family, study their umbral inverses, and introduce [m]-Stirling numbers of the first kind. From the relation between umbral calculus and the Riordan matrices we give several new combinatorial identities

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31

Doran, William F. "Shuffling lattices". Journal of Combinatorial Theory, Series A 66, nr 1 (kwiecień 1994): 118–36. http://dx.doi.org/10.1016/0097-3165(94)90054-x.

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32

WYSOCZAŃSKI, JANUSZ. "MONOTONIC INDEPENDENCE ASSOCIATED WITH PARTIALLY ORDERED SETS". Infinite Dimensional Analysis, Quantum Probability and Related Topics 10, nr 01 (marzec 2007): 17–41. http://dx.doi.org/10.1142/s0219025707002609.

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A generalization of Muraki's notion of monotonic independence onto the case of partially ordered index set is given: algebras indexed by chains are monotonically independent, and algebras indexed by non-comparable elements are boolean independent. Examples of central limit theorem are shown in two cases. For the integral-points lattices ℕd the moments of the limit measure are related to the combinatorics of the finite heap-ordered labelled rooted trees (if d = 2). For the integral-points lattice ℕ × ℤd in Minkowski spacetime the limit measure is given by the recurrence of it's moments, which, for the case d = 1 is related to the inverse error function. Various formulas for computing mixed moments are shown to be related to the boolean-monotonic non-crossing pair partitions.

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33

Cignoli, Roberto. "Quantifiers on distributive lattices". Discrete Mathematics 96, nr 3 (grudzień 1991): 183–97. http://dx.doi.org/10.1016/0012-365x(91)90312-p.

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34

Messinger, M. E., R. J. Nowakowski i P. Prałat. "Elimination schemes and lattices". Discrete Mathematics 328 (sierpień 2014): 63–70. http://dx.doi.org/10.1016/j.disc.2014.03.024.

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35

Yao, Haiyuan, i Heping Zhang. "Non-matchable distributive lattices". Discrete Mathematics 338, nr 3 (marzec 2015): 122–32. http://dx.doi.org/10.1016/j.disc.2014.10.020.

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36

Rajhi, A. "Groups whose lattices of normal subgroups are factorial". Algebra and Discrete Mathematics 30, nr 2 (2020): 239–53. http://dx.doi.org/10.12958/adm1264.

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We prove that the groups G for which the lattice of normal subgroups N(G) is factorial are exactly the UND-groups, that is the groups for which every normal subgroup have a unique normal complement, with finite length.

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37

Chua, Kok Seng, i Patrick Solé. "Eisenstein lattices, Galois rings, and theta series". European Journal of Combinatorics 25, nr 2 (luty 2004): 179–85. http://dx.doi.org/10.1016/s0195-6698(03)00098-2.

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38

Sabidussi, Gert. "On Maps Related to Halin Separation Lattices". European Journal of Combinatorics 6, nr 3 (wrzesień 1985): 257–64. http://dx.doi.org/10.1016/s0195-6698(85)80036-6.

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39

Kahn, Jeff, i Joseph P. S. Kung. "A Classification of Modularly Complemented Geometric Lattices". European Journal of Combinatorics 7, nr 3 (lipiec 1986): 243–48. http://dx.doi.org/10.1016/s0195-6698(86)80029-4.

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40

Droste, Manfred. "Completeness Properties of Certain Normal Subgroup Lattices". European Journal of Combinatorics 8, nr 2 (kwiecień 1987): 129–37. http://dx.doi.org/10.1016/s0195-6698(87)80003-3.

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41

van den Heuvel, J. "Radio Channel Assignment on 2-Dimensional Lattices". Annals of Combinatorics 6, nr 3 (grudzień 2002): 463–77. http://dx.doi.org/10.1007/s000260200017.

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42

Regonati, F., i S. D. Sarti. "Enumeration of Chains in Semi-Primary Lattices". Annals of Combinatorics 4, nr 1 (marzec 2000): 109–24. http://dx.doi.org/10.1007/pl00001272.

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43

Chang, Gerard J., F. K. Hwang, P. E. Wright i J. R. Griggs. "A unique arithmetic labeling of hexagonal lattices". Journal of Combinatorial Designs 3, nr 3 (1995): 169–77. http://dx.doi.org/10.1002/jcd.3180030303.

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44

Chua, Kok Seng, i Patrick Solé. "Jacobi identities, modular lattices, and modular towers". European Journal of Combinatorics 25, nr 4 (maj 2004): 495–503. http://dx.doi.org/10.1016/j.ejc.2003.05.002.

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45

Patras, Frédéric, i Patrick Solé. "The coordinator polynomial of some cyclotomic lattices". European Journal of Combinatorics 28, nr 1 (styczeń 2007): 17–25. http://dx.doi.org/10.1016/j.ejc.2005.10.003.

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46

Kemp, Rowan. "Tableaux and Rank-selection in Fibonacci Lattices". European Journal of Combinatorics 18, nr 2 (luty 1997): 179–93. http://dx.doi.org/10.1006/eujc.1993.0073.

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47

Etienne, G. "On the Möbius Algebra of Geometric Lattices". European Journal of Combinatorics 19, nr 8 (listopad 1998): 921–33. http://dx.doi.org/10.1006/eujc.1998.0227.

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48

Zaslavsky, Thomas. "Supersolvable Frame-matroid and Graphic-lift Lattices". European Journal of Combinatorics 22, nr 1 (styczeń 2001): 119–33. http://dx.doi.org/10.1006/eujc.2000.0418.

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49

Diday, Edwin, i Richard Emilion. "Maximal and stochastic Galois lattices". Discrete Applied Mathematics 127, nr 2 (kwiecień 2003): 271–84. http://dx.doi.org/10.1016/s0166-218x(02)00210-x.

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50

Hochstättler, W., i W. Kern. "Matroid matching in pseudomodular lattices". Combinatorica 9, nr 2 (czerwiec 1989): 145–52. http://dx.doi.org/10.1007/bf02124676.

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