Related papers: An explicit parity theorem for multiple polylogari…

We introduce the Z-polynomial of a matroid, which we define in terms of the Kazhdan-Lusztig polynomial. We then exploit a symmetry of the Z-polynomial to derive a new recursion for Kazhdan-Lusztig coefficients. We solve this recursion,…

The purpose of this paper is to present some multidimensional fixed-point theorems and their applications. For this, we provide a multidimensional fixed point theorem and then using this theorem we prove the existence and uniqueness of a…

The object of this short note is to prove a theorem and present a conjecture for the number of even entries in the character table of the symmetric group.

To determine Euler numbers modulo powers of two seems to be a difficult task. In this paper we achieve this and apply the explicit congruence to give a new proof of a classical result due to M. A. Stern.

The notion of multipolynomials was recently introduced and explored by T. Velanga in [10] as an attempt to encompass the theories of polynomials and multi- linear operators. In the present paper we push this subject further, by proving…

We establish an explicit formula for the general solution of the Benjamin-Ono equation on the torus and on the line. Contents 1. Introduction 1 1.1. The Benjamin-Ono equation 1 1.2. The Lax pair 2 1.3. The explicit formula on the torus 3…

In this paper, we present a generalization of one of the theorems in [G. E. Andrews, Partitions with parts separated by parity, \textit{Annals of Combinatorics} \textbf{23}(2019), 241 - 248], and give its bijective proof. Further variations…

In this paper, we prove several generalizations and applications of a fixed point theorem. This theorem is used to prove the existence and uniqueness of solutions of the linear sparse matrix problem considered.

We prove some generalizations of the sum formula for multiple zeta values by using Hiroyuki Ochiai's method of proving the sum formula.

We prove an easy but interesting result about the linear independence of multiple zeta values of different weights.

A new mechanism for the parity doublers in hadrons is suggested.

This paper considers the problem of the valuation for integer numbers of the zeta function and of five other functions which are naturally associated to it. A relatively elementary approach is exposed, which closely connects this still…

We prove a kind of integral expressions for finite multiple harmonic sums and multiple zeta-star values. Moreover, we introduce a class of multiple integrals, associated with some combinatorial data (called 2-labeled posets). This class…

We prove some new evaluations for multiple polylogarithms of arbitrary depth. The simplest of our results is a multiple zeta evaluation one order of complexity beyond the well-known Broadhurst-Zagier formula. Other results we provide settle…

The duality relation of one-variable multiple polylogarithms was proved by Hirose, Iwaki, Sato and Tasaka by means of iterated integrals. In this paper, we give a new proof using the method of connected sums, which was recently invented by…

In 1993, E. Lesigne proved a polynomial extension of the Wiener-Wintner ergodic theorem and asked two questions: does this result have a uniform counterpart and can an assumption of total ergodicity be replaced by ergodicity? The purpose of…

The complexity of parity games is a long standing open problem that saw a major breakthrough in 2017 when two quasi-polynomial algorithms were published. This article presents a third, independent approach to solving parity games in…

In this paper has been proved the pluripolarity of graphs of algebroid functions

In this paper, we show a generalized Join theorem for real analytic singularities. For complex singularities, this theorem was proved by A. N\'emethi.

In this paper, we explain several conjectures about how a product of two Carlitz-Goss zeta values can be expressed as a F_p-linear combination of Thakur's multizeta values, generalizing the q=2 case dealt by D. Thakur in Relations between…