Related papers: A multiset hook length formula and some applicatio…
We obtain a weighted sum formula of the zeta values at even arguments, and a weighted sum formula of the multiple zeta values with even arguments and its zeta-star analogue. The weight coefficients are given by (symmetric) polynomials of…
It was shown by V. Bergelson that any set B with positive upper multiplicative density contains nicely intertwined arithmetic and geometric progressions: For each positive integer k there exist integers a,b,d such that $ {b(a+id)^j:i,j…
Two general methods for establishing the logarithmic behavior of recursively defined sequences of real numbers are presented. One is the interlacing method, and the other one is based on calculus. Both methods are used to prove logarithmic…
It's well known that multiple polylogarithms give rise to good unipotent variations of mixed Hodge-Tate structures. In this paper we shall {\em explicitly} determine these structures related to multiple logarithms and some other multiple…
We exhibit a bijection between recently-introduced combinatorial objects known as valid hook configurations and certain weighted set partitions. When restricting our attention to set partitions that are matchings, we obtain three new…
The conjecture, still widely open, posed by Marco Buratti, Peter Horak and Alex Rosa states that a list $L$ of $v-1$ positive integers not exceeding $\left\lfloor \frac{v}{2}\right\rfloor$ is the list of edge-lengths of a suitable…
Algorithms to generate various combinatorial structures find tremendous importance in computer science. In this paper, we begin by reviewing an algorithm proposed by Rohl that generates all unique permutations of a list of elements which…
Nakada's colored hook formula is a vast generalization of many important formulae in combinatorics, such as the classical hook length formula and the Peterson's formula for the number of reduced expressions of minuscule Weyl group elements.…
This paper finds relationships between multiple logarithms with a dihedral group action on the arguments. I generalize the combinatorics developed in Gangl, Goncharov and Levin's R-deco polygon representation of multiple logarithms to find…
In this paper, we list several interesting structures of cyclotomic polynomials: specifically relations among blocks obtained by suitable partition of cyclotomic polynomials. We present explicit and self-contained proof for all of them,…
Scattering lengths for d-d, n-$^3$He and p-$^3$H systems are computed via Cluster Reduction Method for Yakubovsky equations in configuration space taking into account Coulomb interaction between protons. MT I-III potential model was used to…
Let $k$ and $i_1,\ldots,i_n$ be natural numbers. Place $k$ balls into a multidimensional box of $i_1\times\cdots \times i_n$ cells, no more than one ball to each cell, such that the projections to each of the coordinate axes have…
The volume of a cyclic polytope can be obtained by forming an iterated integral along a suitable piecewise linear path running through its edges. Different choices of such a path are related by the action of a subgroup of the combinatorial…
A linear code over $\mathbb{F}_q$ with the Hamming metric is called $\Delta$-divisible if the weights of all codewords are divisible by $\Delta$. They have been introduced by Harold Ward a few decades ago. Applications include subspace…
We prove the Ohno-type relation for the interpolated multiple zeta values, which was introduced first by Yamamoto. Same type results for finite multiple zeta values are also given. Moreover, these relations give the sum formula for…
We derive the asymptotic formula for $p_n(N,M)$, the number of partitions of integer $n$ with part size at most $N$ and length at most $M$. We consider both $N$ and $M$ are comparable to $\sqrt{n}$. This is an extension of the classical…
In this paper, we consider the asymptotic properties of hook numbers of partitions in restricted classes. More specifically, we compare the frequency with which partitions into odd parts and partitions into distinct parts have hook numbers…
In this work we obtain recurrent formulae for the number of permutations with either increasing or monotonic (i.e., both increasing and decreasing) runs of bounded length. Our formulae allow one to efficiently compute the number of such…
According to Hoffman's (2,3)-conjecture, the so-called double shuffle relations should imply that every multiple zeta value should express effectively in terms of multizetas whose entries are equal to either 2 or 3, with some explicitly…
Motivated by a formula of A. Postnikov relating binary trees, we define the hook length polynomials for m-ary trees and plane forests, and show that these polynomials have a simple binomial expression. An integer value of this expression is…