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Journal articles on the topic 'Regular polynomial'

Author: Grafiati

Published: 26 October 2022

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1

Merikoski, Jorma K. "Regular polygons, Morgan-Voyce polynomials, and Chebyshev polynomials." Notes on Number Theory and Discrete Mathematics 27, no. 2 (June 2021): 79–87. http://dx.doi.org/10.7546/nntdm.2021.27.2.79-87.

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We say that a monic polynomial with integer coefficients is a polygomial if its each zero is obtained by squaring the edge or a diagonal of a regular n-gon with unit circumradius. We find connections of certain polygomials with Morgan-Voyce polynomials and further with Chebyshev polynomials of second kind.

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2

Lee, Jae-Ho. "Nonsymmetric Askey–Wilson polynomials and Q -polynomial distance-regular graphs." Journal of Combinatorial Theory, Series A 147 (April 2017): 75–118. http://dx.doi.org/10.1016/j.jcta.2016.11.006.

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3

Carballosa, Walter, José M. Rodríguez, José M. Sigarreta, and Yadira Torres-Nuñez. "Alliance polynomial of regular graphs." Discrete Applied Mathematics 225 (July 2017): 22–32. http://dx.doi.org/10.1016/j.dam.2017.03.016.

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4

Meleshkin, A. V. "Regular semigroups of polynomial growth." Mathematical Notes of the Academy of Sciences of the USSR 47, no. 2 (February 1990): 152–58. http://dx.doi.org/10.1007/bf01156824.

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5

Berthomieu, Jérémy, Jean-Charles Faugère, and Ludovic Perret. "Polynomial-time algorithms for quadratic isomorphism of polynomials: The regular case." Journal of Complexity 31, no. 4 (August 2015): 590–616. http://dx.doi.org/10.1016/j.jco.2015.04.001.

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6

Dickie, Garth A. "Twice Q-Polynomial Distance-Regular Graphs." Journal of Combinatorial Theory, Series B 68, no. 1 (September 1996): 161–66. http://dx.doi.org/10.1006/jctb.1996.0061.

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7

Golasiński, Marek, and Francisco Gómez Ruiz. "Polynomial and Regular Maps into Grassmannians." K-Theory 26, no. 1 (May 2002): 51–68. http://dx.doi.org/10.1023/a:1016305323458.

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8

Caughman IV, John S. "Bipartite Q -Polynomial Distance-Regular Graphs." Graphs and Combinatorics 20, no. 1 (March 1, 2004): 47–57. http://dx.doi.org/10.1007/s00373-003-0538-8.

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9

Galetto, Federico, Anthony Vito Geramita, and David Louis Wehlau. "Degrees of Regular Sequences With a Symmetric Group Action." Canadian Journal of Mathematics 71, no. 03 (January 7, 2019): 557–78. http://dx.doi.org/10.4153/cjm-2017-035-3.

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AbstractWe consider ideals in a polynomial ring that are generated by regular sequences of homogeneous polynomials and are stable under the action of the symmetric group permuting the variables. In previous work, we determined the possible isomorphism types for these ideals. Following up on that work, we now analyze the possible degrees of the elements in such regular sequences. For each case of our classification, we provide some criteria guaranteeing the existence of regular sequences in certain degrees.

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10

Birget, J. C. "Semigroups and one-way functions." International Journal of Algebra and Computation 25, no. 01n02 (February 2015): 3–36. http://dx.doi.org/10.1142/s0218196715400019.

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We study the complexity classes 𝖯 and 𝖭𝖯 through a semigroup 𝖿𝖯 ("polynomial-time functions"), consisting of all polynomially balanced polynomial-time computable partial functions. The semigroup 𝖿𝖯 is non-regular if and only if 𝖯 ≠ 𝖭𝖯. The one-way functions considered here are based on worst-case complexity (they are not cryptographic); they are exactly the non-regular elements of 𝖿𝖯. We prove various properties of 𝖿𝖯, e.g. that it is finitely generated. We define reductions with respect to which certain universal one-way functions are 𝖿𝖯-complete.

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11

DIAO, Y., G. HETYEI, and K. HINSON. "TUTTE POLYNOMIALS OF TENSOR PRODUCTS OF SIGNED GRAPHS AND THEIR APPLICATIONS IN KNOT THEORY." Journal of Knot Theory and Its Ramifications 18, no. 05 (May 2009): 561–89. http://dx.doi.org/10.1142/s0218216509007075.

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It is well-known that the Jones polynomial of an alternating knot is closely related to the Tutte polynomial of a special graph obtained from a regular projection of the knot. Relying on the results of Bollobás and Riordan, we introduce a generalization of Kauffman's Tutte polynomial of signed graphs for which describing the effect of taking a signed tensor product of signed graphs is very simple. We show that this Tutte polynomial of a signed tensor product of signed graphs may be expressed in terms of the Tutte polynomials of the original signed graphs by using a simple substitution rule. Our result enables us to compute the Jones polynomials of some large non-alternating knots. The combinatorics used to prove our main result is similar to Tutte's original way of counting "activities" and specializes to a new, perhaps simpler proof of the known formulas for the ordinary Tutte polynomial of the tensor product of unsigned graphs or matroids.

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12

Fernando, José F., and J. M. Gamboa. "Polynomial and regular images of ℝ n." Israel Journal of Mathematics 153, no. 1 (December 2006): 61–92. http://dx.doi.org/10.1007/bf02771779.

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13

Lewis, Heather A. "Homotopy in Q-polynomial distance-regular graphs." Discrete Mathematics 223, no. 1-3 (August 2000): 189–206. http://dx.doi.org/10.1016/s0012-365x(00)00045-5.

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14

Dickie, Garth A., and Paul M. Terwilliger. "Dual Bipartite Q-polynomial Distance-regular Graphs." European Journal of Combinatorics 17, no. 7 (October 1996): 613–23. http://dx.doi.org/10.1006/eujc.1996.0052.

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15

Miklavič, Štefko. "On bipartite Q-polynomial distance-regular graphs." European Journal of Combinatorics 28, no. 1 (January 2007): 94–110. http://dx.doi.org/10.1016/j.ejc.2005.09.003.

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16

Deutsch, Emeric, and Juan A. Rodríguez-Velázquez. "The Hosoya polynomial of distance-regular graphs." Discrete Applied Mathematics 178 (December 2014): 153–56. http://dx.doi.org/10.1016/j.dam.2014.06.018.

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17

De Bruyn, Bart, and Frederic Vanhove. "On Q-polynomial regular near 2d-gons." Combinatorica 35, no. 2 (September 29, 2014): 181–208. http://dx.doi.org/10.1007/s00493-014-3039-x.

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18

Beezer, Robert A., and E. J. Farrell. "The matching polynomial of a regular graph." Discrete Mathematics 137, no. 1-3 (January 1995): 7–18. http://dx.doi.org/10.1016/0012-365x(93)e0125-n.

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19

Chen, Zhenghong, Xiaoxian Tang, and Bican Xia. "Generic regular decompositions for parametric polynomial systems." Journal of Systems Science and Complexity 28, no. 5 (July 30, 2015): 1194–211. http://dx.doi.org/10.1007/s11424-015-3015-6.

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20

Diki, Kamal, Sorin G. Gal, and Irene Sabadini. "Polynomial Approximation in Slice Regular Fock Spaces." Complex Analysis and Operator Theory 13, no. 6 (December 14, 2018): 2729–46. http://dx.doi.org/10.1007/s11785-018-0878-2.

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21

Ahmed, Elsayed, and Dmytro Savchuk. "Endomorphisms of regular rooted trees induced by the action of polynomials on the ring ℤd of d-adic integers." Journal of Algebra and Its Applications 19, no. 08 (August 19, 2019): 2050154. http://dx.doi.org/10.1142/s0219498820501546.

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We show that every polynomial in [Formula: see text] defines an endomorphism of the [Formula: see text]-ary rooted tree induced by its action on the ring [Formula: see text] of [Formula: see text]-adic integers. The sections of this endomorphism also turn out to be induced by polynomials in [Formula: see text] of the same degree. In the case of permutational polynomials acting on [Formula: see text] by bijections, the induced endomorphisms are automorphisms of the tree. In the case of [Formula: see text], such polynomials were completely characterized by Rivest in [Permutation polynomials modulo [Formula: see text], Finite Fields Appl. 7(2) (2001) 287–292]. As our main application, we utilize the result of Rivest to derive the condition on the coefficients of a permutational polynomial [Formula: see text] that is necessary and sufficient for [Formula: see text] to induce a level transitive automorphism of the binary tree, which is equivalent to the ergodicity of the action of [Formula: see text] on [Formula: see text] with respect to the normalized Haar measure.

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22

Beezer, Robert A., and E. J. Farrell. "The matching polynomial of a distance-regular graph." International Journal of Mathematics and Mathematical Sciences 23, no. 2 (2000): 89–97. http://dx.doi.org/10.1155/s0161171200000740.

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A distance-regular graph of diameterdhas2dintersection numbers that determine many properties of graph (e.g., its spectrum). We show that the first six coefficients of the matching polynomial of a distance-regular graph can also be determined from its intersection array, and that this is the maximum number of coefficients so determined. Also, the converse is true for distance-regular graphs of small diameter—that is, the intersection array of a distance-regular graph of diameter 3 or less can be determined from the matching polynomial of the graph.

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23

HAN, YO-SUB, YAJUN WANG, and DERICK WOOD. "INFIX-FREE REGULAR EXPRESSIONS AND LANGUAGES." International Journal of Foundations of Computer Science 17, no. 02 (April 2006): 379–93. http://dx.doi.org/10.1142/s0129054106003887.

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We study infix-free regular languages. We observe the structural properties of finite-state automata for infix-free languages and develop a polynomial-time algorithm to determine infix-freeness of a regular language using state-pair graphs. We consider two cases: 1) A language is specified by a nondeterministic finite-state automaton and 2) a language is specified by a regular expression. Furthermore, we examine the prime infix-free decomposition of infix-free regular languages and design an algorithm for the infix-free primality test of an infix-free regular language. Moreover, we show that we can compute the prime infix-free decomposition in polynomial time. We also demonstrate that the prime infix-free decomposition is not unique.

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24

Gruber, Hermann, and Markus Holzer. "Language operations with regular expressions of polynomial size." Theoretical Computer Science 410, no. 35 (August 2009): 3281–89. http://dx.doi.org/10.1016/j.tcs.2009.04.009.

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25

Pascasio, Arlene A. "A characterization of Q-polynomial distance-regular graphs." Discrete Mathematics 308, no. 14 (July 2008): 3090–96. http://dx.doi.org/10.1016/j.disc.2007.08.034.

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26

Miklavič, Štefko. "Q-polynomial distance-regular graphs with a1=0." European Journal of Combinatorics 25, no. 7 (October 2004): 911–20. http://dx.doi.org/10.1016/j.ejc.2004.02.001.

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27

Dickie, Garth A. "Twice Q-polynomial distance-regular graphs are thin." European Journal of Combinatorics 16, no. 6 (November 1995): 555–60. http://dx.doi.org/10.1016/0195-6698(95)90037-3.

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28

GAWRYCHOWSKI, PAWEŁ, DALIA KRIEGER, NARAD RAMPERSAD, and JEFFREY SHALLIT. "FINDING THE GROWTH RATE OF A REGULAR OR CONTEXT-FREE LANGUAGE IN POLYNOMIAL TIME." International Journal of Foundations of Computer Science 21, no. 04 (August 2010): 597–618. http://dx.doi.org/10.1142/s0129054110007441.

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We give an O(n + t) time algorithm to determine whether an NFA with n states and t transitions accepts a language of polynomial or exponential growth. Given an NFA accepting a language of polynomial growth, we can also determine the order of polynomial growth in O(n+t) time. We also give polynomial time algorithms to solve these problems for context-free grammars.

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29

Popescu, Gelu. "Wold decompositions for representations of C∗-algebras associated with noncommutative varieties." Journal of Operator Theory 87, no. 1 (December 15, 2021): 41–81. http://dx.doi.org/10.7900/jot.2020jun29.2289.

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Given a set Q of polynomials in noncommutative indeterminates Z1,…,Zn and a regular domain Dmp(H)⊂B(H)n, m,n∈N, associated with a positive regular polynomial p∈C⟨Z1,…,Zn⟩, we consider the variety VQ(H):={X=(X1,…,Xn)∈Dmp(H):g(X)=0 for all g∈Q}. Each variety VQ(H) admits a {\it universal model} B=(B1,…,Bn). The main goal of the paper is to study the structure of the ∗-representations of the C∗-algebra C∗(VQ) generated by B1,…,Bn and the identity.

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30

Ramane, Harishchandra S., Shaila B. Gudimani, and Sumedha S. Shinde. "Signless Laplacian Polynomial and Characteristic Polynomial of a Graph." Journal of Discrete Mathematics 2013 (January 3, 2013): 1–4. http://dx.doi.org/10.1155/2013/105624.

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The signless Laplacian polynomial of a graph G is the characteristic polynomial of the matrix Q(G)=D(G)+A(G), where D(G) is the diagonal degree matrix and A(G) is the adjacency matrix of G. In this paper we express the signless Laplacian polynomial in terms of the characteristic polynomial of the induced subgraphs, and, for regular graph, the signless Laplacian polynomial is expressed in terms of the derivatives of the characteristic polynomial. Using this we obtain the characteristic polynomial of line graph and subdivision graph in terms of the characteristic polynomial of induced subgraphs.

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31

Fenton, Peter, Janne Grohn, Janne Heittokangas, John Rossi, and Jouni Rattya. "On α-Polynomial Regular Functions, with Applications to Ordinary Differential Equations." Proceedings of the Edinburgh Mathematical Society 57, no. 2 (March 13, 2014): 405–21. http://dx.doi.org/10.1017/s0013091514000017.

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AbstractThis research deals with properties of polynomial regular functions, which were introduced in a recent study concerning Wiman-Valiron theory in the unit disc. The relation of polynomial regular functions to a number of function classes is investigated. Of particular interest is the connection to the growth class Gα, which is closely associated with the theory of linear differential equations with analytic coefficients in the unit disc. If the coefficients are polynomial regular functions, then it turns out that a finite set of real numbers containing all possible maximum modulus orders of solutions can be found. This is in contrast to what is known about the case when the coefficients belong to Gα.

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32

Klimek, Maciej. "Iteration of Analytic Multifunctions." Nagoya Mathematical Journal 162 (June 2001): 19–40. http://dx.doi.org/10.1017/s0027763000007789.

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It is shown that iteration of analytic set-valued functions can be used to generate composite Julia sets in CN. Then it is shown that the composite Julia sets generated by a finite family of regular polynomial mappings of degree at least 2 in CN, depend analytically on the generating polynomials, in the sense of the theory of analytic set-valued functions. It is also proved that every pluriregular set can be approximated by composite Julia sets. Finally, iteration of infinitely many polynomial mappings is used to give examples of pluriregular sets which are not composite Julia sets and on which Markov’s inequality fails.

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33

Sghaier, Mabrouk. "Some symmetric semi-classical polynomial sets." Filomat 25, no. 3 (2011): 175–89. http://dx.doi.org/10.2298/fil1103175s.

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We show that if ? is a regular semi-classical form (linear functional), then the symmetric form u defined by the relation x?u=??? where ?u is the even part of u, is also regular and semi-classical form for every complex ? except for a discrete set of numbers depending on ?. We give explicitly the recurrence coefficients, integral representation and the structure relation coefficients of the orthogonal polynomials sequence associated with u and the class of the form u knowing that of ?. We conclude with some illustrative examples.

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34

Lu, Pengli, Ke Gao, and Yang Yang. "Generalized Characteristic Polynomials of Join Graphs and Their Applications." Discrete Dynamics in Nature and Society 2017 (2017): 1–10. http://dx.doi.org/10.1155/2017/2372931.

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The Kirchhoff index ofGis the sum of resistance distances between all pairs of vertices ofGin electrical networks.LEL(G)is the Laplacian-Energy-Like Invariant ofGin chemistry. In this paper, we define two classes of join graphs: the subdivision-vertex-vertex joinG1⊚G2and the subdivision-edge-edge joinG1⊝G2. We determine the generalized characteristic polynomial of them. We deduce the adjacency (Laplacian and signless Laplacian, resp.) characteristic polynomials ofG1⊚G2andG1⊝G2whenG1isr1-regular graph andG2isr2-regular graph. As applications, the Laplacian spectra enable us to get the formulas of the number of spanning trees, Kirchhoff index, andLELofG1⊚G2andG1⊝G2in terms of the Laplacian spectra ofG1andG2.

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35

Belousov, I. N., A. A. Makhnev, and M. S. Nirova. "On $Q$-polynomial distance-regular graphs $\Gamma$ with strongly regular graphs $\Gamma_2$ and $\Gamma_3$." Sibirskie Elektronnye Matematicheskie Izvestiya 16 (October 7, 2019): 1385–92. http://dx.doi.org/10.33048/semi.2019.16.096.

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36

Carballosa, Walter, José M. Rodríguez, José M. Sigarreta, and Yadira Torres-Nuñez. "Distinctive power of the alliance polynomial for regular graphs." Electronic Notes in Discrete Mathematics 46 (September 2014): 313–20. http://dx.doi.org/10.1016/j.endm.2014.08.041.

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37

Bedford, Eric, and Mattias Jonsson. "Dynamics of regular polynomial endomorphisms of C k [superscript]." American Journal of Mathematics 122, no. 1 (2000): 153–212. http://dx.doi.org/10.1353/ajm.2000.0001.

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38

Alghamdi, Azza, Maciej Klimek, and Marta Kosek. "Attractors of Compactly Generated Semigroups of Regular Polynomial Mappings." Complexity 2018 (November 11, 2018): 1–11. http://dx.doi.org/10.1155/2018/5698021.

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We investigate the metric space of pluriregular sets as well as the contractions on that space induced by infinite compact families of proper polynomial mappings of several complex variables. The topological semigroups generated by such families, with composition as the semigroup operation, lead to the constructions of a variety of Julia-type pluriregular sets. The generating families can also be viewed as infinite iterated function systems with compact attractors. We show that such attractors can be approximated both deterministically and probabilistically in a manner of the classic chaos game.

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39

Case, John, Sanjay Jain, Rüdiger Reischuk, Frank Stephan, and Thomas Zeugmann. "Learning a subclass of regular patterns in polynomial time." Theoretical Computer Science 364, no. 1 (November 2006): 115–31. http://dx.doi.org/10.1016/j.tcs.2006.07.044.

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40

Fernando, José F. "On the one dimensional polynomial and regular images of." Journal of Pure and Applied Algebra 218, no. 9 (September 2014): 1745–53. http://dx.doi.org/10.1016/j.jpaa.2014.01.011.

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41

Cohen, Stephen D. "Polynomial Factorisation and an Application to Regular Directed Graphs." Finite Fields and Their Applications 4, no. 4 (October 1998): 316–46. http://dx.doi.org/10.1006/ffta.1998.0219.

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42

Caughman, John S. "Bipartite Q-Polynomial Quotients of Antipodal Distance-Regular Graphs." Journal of Combinatorial Theory, Series B 76, no. 2 (July 1999): 291–96. http://dx.doi.org/10.1006/jctb.1999.1911.

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43

Miklavič, Štefko, and Paul Terwilliger. "Bipartite Q-polynomial distance-regular graphs and uniform posets." Journal of Algebraic Combinatorics 38, no. 2 (October 9, 2012): 225–42. http://dx.doi.org/10.1007/s10801-012-0401-1.

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44

Jurišić, Aleksandar, Paul Terwilliger, and Arjana Žitnik. "The Q-polynomial idempotents of a distance-regular graph." Journal of Combinatorial Theory, Series B 100, no. 6 (November 2010): 683–90. http://dx.doi.org/10.1016/j.jctb.2010.07.002.

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45

Urlep, Matjaž. "Triple intersection numbers of Q-polynomial distance-regular graphs." European Journal of Combinatorics 33, no. 6 (August 2012): 1246–52. http://dx.doi.org/10.1016/j.ejc.2012.02.005.

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46

Pascasio, Arlene A. "Tight Distance-Regular Graphs and the Q-Polynomial Property." Graphs and Combinatorics 17, no. 1 (March 31, 2001): 149–69. http://dx.doi.org/10.1007/s003730170063.

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47

Ma, JianMin, and Jack H. Koolen. "Twice Q-polynomial distance-regular graphs of diameter 4." Science China Mathematics 58, no. 12 (December 7, 2014): 2683–90. http://dx.doi.org/10.1007/s11425-014-4958-0.

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48

Leonard, Douglas A. "Directed distance regular graphs with the Q-polynomial property." Journal of Combinatorial Theory, Series B 48, no. 2 (April 1990): 191–96. http://dx.doi.org/10.1016/0095-8956(90)90117-i.

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49

Yanagimoto, Tomoko. "Gamma-polynomial and its generalization to a 2-string tangle polynomial." Journal of Knot Theory and Its Ramifications 24, no. 08 (July 2015): 1550047. http://dx.doi.org/10.1142/s0218216515500479.

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The zeroth coefficient polynomial of the skein (HOMFLYPT) knot polynomial called the Γ-polynomial is studied from a viewpoint of regular homotopy of knot diagrams. In particular, an elementary existence proof of the knot invariance of the Γ-polynomial is given. After observing that there are three types for 2-string tangle diagrams, the Γ-polynomial is generalized to a polynomial invariant of a 2-string tangle. As an application, we have a new proof of the assertion that Kinoshita's θ-curve is not equivalent to the trivial θ-curve.

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50

ISHII, ATSUSHI. "ON NORMALIZATIONS OF A REGULAR ISOTOPY INVARIANT FOR SPATIAL GRAPHS." International Journal of Mathematics 22, no. 11 (November 2011): 1545–59. http://dx.doi.org/10.1142/s0129167x1100729x.

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We give a framework to normalize a regular isotopy invariant of a spatial graph, and introduce many normalizations satisfying the same relation under a local move. We normalize the Yamada polynomial for spatial embeddings of almost all trivalent graphs without a bridge, and see the benefit to utilize our normalizations from the viewpoint of skein relations, the finite type invariants, and evaluations of the Yamada polynomial. We show that the collection of the differences between two of our normalizations is a complete spatial-graph-homology invariant.

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