Results 41 to 50 of about 1,248 (76)
Consequences of a sextuple‐product identity
International Journal of Mathematics and Mathematical Sciences, Volume 10, Issue 3, Page 545-549, 1987., 1987 A sextuple‐product identity, which essentially results from squaring the classical Gauss‐Jacobi triple‐product identity, is used to derive two trigonometrical identities. Several special cases of these identities are then presented and discussed.
John A. Ewell
wiley +1 more source
The 26 Wilf-equivalence classes of length five quasi-consecutive patterns [PDF]
Discrete Mathematics & Theoretical Computer Science, 2018 We present two families of Wilf-equivalences for consecutive and quasi-consecutive vincular patterns. These give new proofs of the classification of consecutive patterns of length $4$ and $5$.
Evan Chen, Shyam Narayanan
doaj +1 more source
Fully degenerate poly-Bernoulli numbers and polynomials
Open Mathematics, 2016 In this paper, we introduce the new fully degenerate poly-Bernoulli numbers and polynomials and inverstigate some properties of these polynomials and numbers.
Kim Taekyun, Kim Dae San, Seo Jong-Jin
doaj +1 more source
Continued fractions for permutation statistics [PDF]
Discrete Mathematics & Theoretical Computer Science, 2018 We explore a bijection between permutations and colored Motzkin paths that has been used in different forms by Foata and Zeilberger, Biane, and Corteel.
Sergi Elizalde
doaj +1 more source
Fourier series of functions involving higher-order ordered Bell polynomials
Open Mathematics, 2017 In 1859, Cayley introduced the ordered Bell numbers which have been used in many problems in number theory and enumerative combinatorics. The ordered Bell polynomials were defined as a natural companion to the ordered Bell numbers (also known as the ...
Kim Taekyun +3 more
doaj +1 more source
CANONICAL REPRESENTATIVES FOR DIVISOR CLASSES ON TROPICAL CURVES AND THE MATRIX–TREE THEOREM
Forum of Mathematics, Sigma, 2014 Let $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit ...
YANG AN +3 more
doaj +1 more source
Lattice paths with catastrophes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2017 In queuing theory, it is usual to have some models with a "reset" of the queue. In terms of lattice paths, it is like having the possibility of jumping from any altitude to zero.
Cyril Banderier, Michael Wallner
doaj +1 more source
New harmonic number identities with applications [PDF]
, 2009 We determine the explicit formulas for the sum of products of homogeneous multiple harmonic sums $\sum_{k=1}^n \prod_{j=1}^r H_k(\{1\}^{\lambda_j})$ when $\sum_{j=1}^r \lambda_j\leq 5$.
Tauraso, Roberto
core +3 more sources
Some vanishing sums involving binomial coefficients in the denominator [PDF]
, 2008 Identities involving binomial coeffcients usually arise in situations where counting is carried out in two different ways. For instance, some identities obtained by William Horrace [1] using probability theory turn out to be special cases of the Chu ...
Purkait, S. (Soma), Sury, B.
core
Key-avoidance for alternating sign matrices [PDF]
Discrete Mathematics & Theoretical Computer ScienceWe initiate a systematic study of key-avoidance on alternating sign matrices (ASMs) defined via pattern-avoidance on an associated permutation called the \emph{key} of an ASM.
Mathilde Bouvel +2 more
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