Results 21 to 30 of about 1,353 (123)
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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A new proof of some identities of Bressoud
International Journal of Mathematics and Mathematical Sciences, Volume 32, Issue 10, Page 627-633, 2002., 2002 We provide a new proof of the following two identities due to Bressoud: ∑m=0Nqm2[Nm]=∑m=−∞∞(−1)mqm(51m+)/2 [ 2NN+2m], ∑m=0Nqm2+m[Nm]=(1/(1−qN+1))∑m=−∞∞(−1)m×qm(53m+)/2 [ 22N+N+22m+], which can be considered as finite versions of the Rogers‐Ramanujan identities.
Robin Chapman
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Evaluation of integrals with hypergeometric and logarithmic functions
Open Mathematics, 2018 We provide an explicit analytical representation for a number of logarithmic integrals in terms of the Lerch transcendent function and other special functions.
Sofo Anthony
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Some combinatorial matrices and their LU-decomposition
Special Matrices, 2020 Three combinatorial matrices were considered and their LU-decompositions were found. This is typically done by (creative) guessing, and the proofs are more or less routine calculations.
Prodinger Helmut
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A new triple sum combinatorial identity
International Journal of Mathematics and Mathematical Sciences, Volume 31, Issue 12, Page 761-763, 2002., 2002 We prove a new triple sum combinatorial identity derived from rp(x, y, z) = (x+y−z)p − (xp + yp − zp), extending a previous result by Sinyor et al.
Joseph Sinyor, Akalu Tefera
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Symmetry of Narayana Numbers and Rowvacuation of Root Posets
Forum of Mathematics, Sigma, 2021 For a Weyl group W of rank r, the W-Catalan number is the number of antichains of the poset of positive roots, and the W-Narayana numbers refine the W-Catalan number by keeping track of the cardinalities of these antichains.
Colin Defant, Sam Hopkins
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Infinite products over hyperpyramid lattices
International Journal of Mathematics and Mathematical Sciences, Volume 23, Issue 4, Page 271-277, 2000., 2000 New infinite product identities are given, based on summed visible (from the origin) point vectors. Each result is found from summing on vpv lattices dividing space into radial regions from the origin. Recently, Baake et al. and Mosseri considered the 2‐D visible lattice points as part of an optical experiment in which so‐called Optical Fourier ...
Geoffrey B. Campbell
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Patterns in Inversion Sequences I [PDF]
Discrete Mathematics & Theoretical Computer Science, 2016 Permutations that avoid given patterns have been studied in great depth for their connections to other fields of mathematics, computer science, and biology.
Sylvie Corteel +3 more
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Sums of products of Apostol-Bernoulli and Apostol-Euler polynomials
, 2014 In this paper, a further investigation for the Apostol-Bernoulli and Apostol-Euler polynomials and numbers is performed. Some closed formulae of sums of products of any number of Apostol-Bernoulli and Apostol-Euler polynomials and numbers are established
Yuan He, S. Araci
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A closer look at some new identities
International Journal of Mathematics and Mathematical Sciences, Volume 21, Issue 3, Page 581-586, 1998., 1998 We obtain infinite products related to the concept of visible from the origin point vectors. Among these is in which φ3(k) denotes for fixed k, the number of positive integer solutions of (a, b, k) = 1 where a < b < k, assuming (a, b, k) is the gcd(a, b, k).
Geoffrey B. Campbell
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