Results 1 to 10 of about 292 (58)
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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A combinatorial proof of the Gaussian product inequality beyond the MTP2 case
Dependence Modeling, 2022 A combinatorial proof of the Gaussian product inequality (GPI) is given under the assumption that each component of a centered Gaussian random vector X=(X1,…,Xd){\boldsymbol{X}}=\left({X}_{1},\ldots ,{X}_{d}) of arbitrary length can be written as a ...
Genest Christian, Ouimet Frédéric
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The Kraft sum as a monotone function on the refinement-ordered set of uniquely decipherable codes [PDF]
, 2013 The set of all uniquely decipherable (UD) codes is partially ordered by re nement, meaning that all strings in the cruder code can be represented as con- catenations of strings taken from the ner code.
Foldes, Stephan
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Compositions inside a rectangle and unimodality [PDF]
, 2007 Let c^{k,l}(n) be the number of compositions (ordered partitions) of the integer n whose Ferrers diagram fits inside a k-by-l rectangle. The purpose of this note is to give a simple, algebraic proof of a conjecture of Vatter that the sequence c^{k,l}(0),
Sagan, Bruce E.
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Antichains and counterpoint dichotomies [PDF]
, 2012 We construct a special type of antichain (i. e., a family of subsets of a set, such that no subset is contained in another) using group-theoretical considerations, and obtain an upper bound on the cardinality of such an antichain.
Agustín-Aquino, Octavio A.
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The Eulerian Distribution on Involutions is Indeed Unimodal [PDF]
, 2005 Let I_{n,k} (resp. J_{n,k}) be the number of involutions (resp. fixed-point free involutions) of {1,...,n} with k descents. Motivated by Brenti's conjecture which states that the sequence I_{n,0}, I_{n,1},..., I_{n,n-1} is log-concave, we prove that the ...
Brenti +10 more
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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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Recurrence Relations for Strongly q-Log-Convex Polynomials [PDF]
, 2008 We consider a class of strongly q-log-convex polynomials based on a triangular recurrence relation with linear coefficients, and we show that the Bell polynomials, the Bessel polynomials, the Ramanujan polynomials and the Dowling polynomials are strongly
Arthur L. B. Yang +6 more
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The hyperbolicity constant of infinite circulant graphs
Open Mathematics, 2017 If X is a geodesic metric space and x1, x2, x3 ∈ X, a geodesic triangle T = {x1, x2, x3} is the union of the three geodesics [x1x2], [x2x3] and [x3x1] in X.
Rodríguez José M., Sigarreta José M.
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On the polyhedral cones of convex and concave vectors [PDF]
, 2013 Convex or concave sequences of n positive terms, viewed as vectors in n-space, constitute convex cones with 2n − 2 and n extreme rays, respectively.
Foldes, Stephan, Major, Laszlo
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