Results 21 to 30 of about 119 (92)
The log-concavity of the q-derangement numbers of type B
Open Mathematics, 2018 Recently, Chen and Xia proved that for n ≥ 6, the q-derangement numbers Dn(q) are log-concave except for the last term when n is even. In this paper, employing a recurrence relation for DnB(q) $\begin{array}{} \displaystyle D^B_n(q) \end{array ...
Liu Eric H., Du Wenjing
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Negative moments of orthogonal polynomials
Forum of Mathematics, Sigma, 2023 If a sequence indexed by nonnegative integers satisfies a linear recurrence without constant terms, one can extend the indices of the sequence to negative integers using the recurrence.
Jihyeug Jang +4 more
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A note on Eulerian numbers and Toeplitz matrices
Special Matrices, 2020 This note presents a new formula of Eulerian numbers derived from Toeplitz matrices via Riordan array approach.
He Tian-Xiao, Shiue Peter J.-S.
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Refined ratio monotonicity of the coordinator polynomials of the root lattice of type Bn
Open Mathematics, 2023 Ratio monotonicity, a property stronger than both log-concavity and the spiral property, describes the behavior of the coefficients of many classical polynomials.
Su Xun-Tuan, Sun Fan-Bo
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Forum of Mathematics, Sigma, 2023 We introduce a new class of permutations, called web permutations. Using these permutations, we provide a combinatorial interpretation for entries of the transition matrix between the Specht and $\operatorname {SL}_2$ -web bases of the irreducible
Byung-Hak Hwang +2 more
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Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations [PDF]
Discrete Mathematics & Theoretical Computer Science, 2021 Defant, Engen, and Miller defined a permutation to be uniquely sorted if it has exactly one preimage under West's stack-sorting map. We enumerate classes of uniquely sorted permutations that avoid a pattern of length three and a pattern of length four by
Hanna Mularczyk
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Veterinary Dermatology, Volume 27, Issue 5, Page 391-e98, October 2016., 2016 Background– Pseudomonas aeruginosa (PA) may cause suppurative otitis externa with severe inflammation and ulceration in dogs. Multidrug resistance is commonly reported for this organism, creating a difficult therapeutic challenge. Objective– The aim of this study was to evaluate the in vitro antimicrobial activity of a gel containing 0.5 µg/mL of ...
Giovanni Ghibaudo +6 more
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Determinantal generating functions of colored spanning forests
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 6, Page 273-283, 2004., 2004 The color type of a spanning forest of a graph with colored edges is defined and, subsequently, it is proved that the generating function of such spanning forests is obtained as the formal expansion of a certain determinant. An analogous determinantal expansion yields the generating function of all spanning forests of a given color type that contain a ...
Gregory M. Constantine, Marius G. Buliga
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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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