Results 21 to 30 of about 1,248 (76)
A new approach to the r-Whitney numbers by using combinatorial differential calculus
Acta Universitatis Sapientiae: Mathematica, 2019 In the present article we introduce two new combinatorial interpretations of the r-Whitney numbers of the second kind obtained from the combinatorics of the differential operators associated to the grammar G := {y → yxm, x → x}.
Méndez Miguel A., Ramírez José L.
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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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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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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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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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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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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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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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Visible point vector summations from hypercube and hyperpyramid lattices
International Journal of Mathematics and Mathematical Sciences, Volume 21, Issue 4, Page 741-748, 1998., 1998 New identities are given, based on ideas related to visible (from the origin) point vectors. Each result was found from summing on vpv lattices dividing space into radial regions from the origin. This is related to recent work by the author in which new partition type infinite products were derived.
Geoffrey B. Campbell
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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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