Results 41 to 50 of about 1,212 (76)

Some congruences involving binomial coefficients

, 2015
Binomial coefficients and central trinomial coefficients play important roles in combinatorics. Let $p>3$ be a prime. We show that $$T_{p-1}\equiv\left(\frac p3\right)3^{p-1}\ \pmod{p^2},$$ where the central trinomial coefficient $T_n$ is the constant ...
Cao, Hui-Qin, Sun, Zhi-Wei
core   +1 more source

A Pipe Dream Perspective on Totally Symmetric Self-Complementary Plane Partitions

Forum of Mathematics, Sigma
We characterize totally symmetric self-complementary plane partitions (TSSCPP) as bounded compatible sequences satisfying a Yamanouchi-like condition. As such, they are in bijection with certain pipe dreams.
Daoji Huang, Jessica Striker
doaj   +1 more source

Proof of two conjectures of Z.-W. Sun on congruences for Franel numbers

, 2012
For all nonnegative integers n, the Franel numbers are defined as $$ f_n=\sum_{k=0}^n {n\choose k}^3.$$ We confirm two conjectures of Z.-W. Sun on congruences for Franel numbers: \sum_{k=0}^{n-1}(3k+2)(-1)^k f_k &\equiv 0 \pmod{2n^2}, \sum_{k=0}^{p-1}(3k+
Calkin N. J., Foata D., Franel J., Franel J., Guo V. J.W., Koepf W., MacMachon P. A., Riordan J., Strehl V., Sun Z.-W., Victor J.W. Guo, Zagier D.   +11 more
core   +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, Kim Dae San, Jang Gwan-Woo, Jang Lee Chae   +3 more
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

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, MATTHEW BAKER, GREG KUPERBERG, FARBOD SHOKRIEH   +3 more
doaj   +1 more source

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  

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

Key-avoidance for alternating sign matrices [PDF]

Discrete Mathematics & Theoretical Computer Science
We 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, Rebecca Smith, Jessica Striker   +2 more
doaj   +1 more source

Taylor’s series expansions for real powers of two functions containing squares of inverse cosine function, closed-form formula for specific partial Bell polynomials, and series representations for real powers of Pi

Demonstratio Mathematica, 2022
In this article, by virtue of expansions of two finite products of finitely many square sums, with the aid of series expansions of composite functions of (hyperbolic) sine and cosine functions with inverse sine and cosine functions, and in the light of ...
Qi Feng
doaj   +1 more source