Results 21 to 30 of about 69 (69)
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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Differential equations associated with generalized Bell polynomials and their zeros
Open Mathematics, 2016 In this paper, we study differential equations arising from the generating functions of the generalized Bell polynomials.We give explicit identities for the generalized Bell polynomials.
Ryoo Seoung Cheon
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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 generalized formula of Hardy
International Journal of Mathematics and Mathematical Sciences, Volume 17, Issue 2, Page 369-378, 1994., 1994 We give new formulae applicable to the theory of partitions. Recent work suggests they also relate to quasi‐crystal structure and self‐similarity. Other recent work has given continued fractions for the type of functions herein. Hardy originally gave such formulae as ours in early work on gap power series which led to his and Littlewood′s High Indices ...
Geoffrey B. Campbell
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Some recurrence formulas for the Hermite polynomials and their squares
Open Mathematics, 2018 In this paper, by making use of the generating function methods and Padé approximation techniques, we establish some new recurrence formulas for the Hermite polynomials and their squares.
He Yuan, Yang Fengzao
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Discrete Mathematics & Theoretical Computer Science, 2017 Given a set $Y$ of decreasing plane trees and a permutation $\pi$, how many trees in $Y$ have $\pi$ as their postorder? Using combinatorial and geometric constructions, we provide a method for answering this question for certain sets $Y$ and all ...
Colin Defant
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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
wiley +1 more source