Results 31 to 40 of about 2,046 (100)
Counting occurrences of 132 in an even permutation
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 25, Page 1329-1341, 2004., 2004 We study the generating function for the number of even (or odd) permutations on n letters containing exactly r ≥ 0 occurrences of a 132 pattern. It is shown that finding this function for a given r amounts to a routine check of all permutations in 𝔖2r.
Toufik Mansour
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Descent c-Wilf Equivalence [PDF]
Discrete Mathematics & Theoretical Computer Science, 2017 Let $S_n$ denote the symmetric group. For any $\sigma \in S_n$, we let $\mathrm{des}(\sigma)$ denote the number of descents of $\sigma$, $\mathrm{inv}(\sigma)$ denote the number of inversions of $\sigma$, and $\mathrm{LRmin}(\sigma)$ denote the number of
Quang T. Bach, Jeffrey B. Remmel
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First hitting times of simple random walks on graphs with congestion points
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 30, Page 1911-1922, 2003., 2003 We derive the explicit formulas of the probability generating functions of the first hitting times of simple random walks on graphs with congestion points using group representations.
Mihyun Kang
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Equivalence classes of mesh patterns with a dominating pattern [PDF]
Discrete Mathematics & Theoretical Computer Science, 2018 Two mesh patterns are coincident if they are avoided by the same set of permutations, and are Wilf-equivalent if they have the same number of avoiders of each length.
Murray Tannock, Henning Ulfarsson
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MacMahon’s statistics on higher-dimensional partitions
Forum of Mathematics, Sigma, 2023 We study some combinatorial properties of higher-dimensional partitions which generalize plane partitions. We present a natural bijection between d-dimensional partitions and d-dimensional arrays of nonnegative integers.
Alimzhan Amanov, Damir Yeliussizov
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Combinatorics of geometrically distributed random variables: new q‐tangent and q‐secant numbers
International Journal of Mathematics and Mathematical Sciences, Volume 24, Issue 12, Page 825-838, 2000., 2000 Up‐down permutations are counted by tangent (respectively, secant) numbers. Considering words instead, where the letters are produced by independent geometric distributions, there are several ways of introducing this concept; in the limit they all coincide with the classical version. In this way, we get some new q‐tangent and q‐secant functions.
Helmut Prodinger
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n‐Color partitions with weighted differences equal to minus two
International Journal of Mathematics and Mathematical Sciences, Volume 20, Issue 4, Page 759-768, 1997., 1997 In this paper we study those n‐color partitions of Agarwal and Andrews, 1987, in which each pair of parts has weighted difference equal to −2 Results obtained in this paper for these partitions include several combinatorial identities, recurrence relations, generating functions, relationships with the divisor function and computer produced tables.
A. K. Agarwal, R. Balasubrananian
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A new class of infinite products, and Euler′s totient
International Journal of Mathematics and Mathematical Sciences, Volume 17, Issue 3, Page 417-422, 1994., 1993 We introduce some new infinite products, the simplest being where ϕk is the set of positive integers less than and relatively prime to k, valid for |y|∧|qy| both less than unity, with q ≠ 1. The idea of a q‐analogue for the Euler totient function is suggested.
Geoffrey B. Campbell
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Snow Leopard Permutations and Their Even and Odd Threads [PDF]
Discrete Mathematics & Theoretical Computer Science, 2016 Caffrey, Egge, Michel, Rubin and Ver Steegh recently introduced snow leopard permutations, which are the anti-Baxter permutations that are compatible with the doubly alternating Baxter permutations. Among other things, they showed that these permutations
Eric S. Egge, Kailee Rubin
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An infinite version of the Pólya enumeration theorem
International Journal of Mathematics and Mathematical Sciences, Volume 15, Issue 4, Page 697-700, 1992., 1991 Using measure theory, the orbit counting form of Pólya′s enumeration theorem is extended to countably infinite discrete groups.
Robert A. Bekes
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