Related papers: Multiple Dedekind Symbols
We introduce ballot matrices, a signed combinatorial structure whose definition naturally follows from the generating function for labeled interval orders. A sign reversing involution on ballot matrices is defined. We show that matrices…
We investigate a general framework of multiplicative multitask feature learning which decomposes each task's model parameters into a multiplication of two components. One of the components is used across all tasks and the other component is…
We present a review of the symbol map, a mathematical tool that can be useful in simplifying expressions among multiple polylogarithms, and recall its main properties. A recipe is given for how to obtain the symbol of a multiple…
We introduce an extension of the standard cohomology which is characterised by maps that fail to be classical cocycles by products of simpler maps. The construction is motivated by the study of Manin's noncommutative modular symbols and of…
The main object of this work is to show how some rather elementary techniques based upon certain inverse pairs of symbolic operators would lead us easily to several decomposition formulas associated with confluent hypergeometric functions…
We treat desingularized multiple zeta-functions introduced by Furusho, Komori, Matsumoto and Tsumura. In this paper, we prove functional relations, which are shuffle type product formulae, between desingularized multiple zeta-functions and…
It is known that there are infinitely many singularities of multiple zeta functions and the special values at non-positive integer points are indeterminate. In order to give a suitable rigorous meaning of the special values there, Furusho,…
We study some divisibility properties of Dedekind numbers. We show that the ninth Dedekind number is congruent to 6 modulo 210.
We introduce new combinatorial objects called the shifted domino tableaux. We prove that these objects are in bijection with pairs of shifted Young tableaux. This bijection shows that shifted domino tableaux can be seen as elements of the…
Some finite series of harmonic numbers involving certain reciprocals are evaluated. Products of such reciprocals are expanded in a sum of the individual reciprocals, leading to a computer program. A list of examples is provided.
We investigate how to model exchangeability with choice functions. Exchangeability is a structural assessment on a sequence of uncertain variables. We show how such assessments are a special indifference assessment, and how that leads to a…
We give an explicit formula for the shuffle relation in a general double shuffle framework that specializes to double shuffle relations of multiple zeta values and multiple polylogarithms. As an application, we generalize the well-known…
This paper establishes mixed multiplicity formulas concerning the relationship between mixed multiplicities of modules and mixed multiplicities of rings via rank of modules.
In this paper, we settle the problem posed by Singer which is on a comparison problem between the renormalized values of shuffle type and of harmonic type of multiple zeta functions.
Dedekind sums have applications in quite a number of fields of mathematics. Therefore, their distribution has found considerable interest. This article gives a survey of several aspects of the distribution of these sums. In particular, it…
This paper presents a detailed symbolic approach to the study of self-similar tilings. It uses properties of addresses associated with graph-directed iterated function systems to establish conjugacy properties of tiling spaces. Tiles may be…
We study the commutation structure within the Pauli groups built on all decompositions of a given Hilbert space dimension $q$, containing a square, into its factors. The simplest illustrative examples are the quartit ($q=4$) and two-qubit…
A reconstruction problem is formulated for multisets over commutative groupoids. The cards of a multiset are obtained by replacing a pair of its elements by their sum. Necessary and sufficient conditions for the reconstructibility of…
An explicit product representation is proved for the correlation function of the multiplicities of closed geodesics on the modular surface. This makes rigorous part of the investigation of Bogomolny, Leyvraz and Schmit on the correlation of…
In this note we consider functions with Moebius-periodic rational coefficients. These functions under some conditions take algebraic values and can be recovered by theta functions and the Dedekind eta function. Special cases are the…