Related papers: Determinants, Choices and Combinatorics
In this article, we prove a weighted version of Saitoh's conjecture. As an application, we prove a weighted version of Saitoh's conjecture for higher derivatives.
The infinitary propositional logic of here-and-there is important for the theory of answer set programming in view of its relation to strongly equivalent transformations of logic programs. We know a formal system axiomatizing this logic…
Given natural numbers m and n, we define a deflation map from the characters of the symmetric group S_{mn} to the characters of S_n. This map is obtained by first restricting a character of S_{mn} to the wreath product S_m \wr S_n, and then…
An elementary rheory of concatenation is introduced and used to establish mutual interpretability of Robinson arithmetic, Minimal Predicative Set Theory, the quantifier-free part of Kirby's finitary set theory, and Adjunctive Set Theory,…
This article is an introduction to combinatorics under the axiom of determinacy with a focus on partition properties and infinity Borel codes.
Rota's basis conjecture (RBC) states that given a collection B of n bases in a matroid M of rank n, one can always find n disjoint rainbow bases with respect to B. We show that if M is a matroid having n + k elements, then one can construct…
In our previous paper, we determined a unified combinatorial framework to look at a large number of colored partition identities, and studied the five identities corresponding to the exceptional modular equations of prime degree of the…
We give a combinatorial classification for the class of postcritically fixed Newton maps of polynomials as dynamical systems. This lays the foundation for classification results of more general classes of Newton maps. A fundamental…
We consider a generalized riffle shuffle on the colored permutation group $G_{p, n}$ and derive a determinantal formula for the probability of finding descents at given positions, proof of which is based on the bijection between the set of…
A combinatorial methods are used to investigate some properties of certain generalized Stirling numbers, including explicit formula and recurrence relations. Furthermore, an expression of these numbers with symmetric function is deduced.
We prove the unbounded denominators conjecture in the theory of noncongruence modular forms for finite index subgroups of SL_2(Z). Our result includes also Mason's generalization of the original conjecture to the setting of vector-valued…
Propositional formulas that are equivalent in intuitionistic logic, or in its extension known as the logic of here-and-there, have the same stable models. We extend this theorem to propositional formulas with infinitely long conjunctions…
We generalise the existence of combinatorial designs to the setting of subset sums in lattices with coordinates indexed by labelled faces of simplicial complexes. This general framework includes the problem of decomposing hypergraphs with…
A classical question of propositional logic is one of the shortest proof of a tautology. A related fundamental problem is to determine the relative efficiency of standard proof systems, where the relative complexity is measured using the…
The goal of this paper is to lay the foundations for a combinatorial study, via orthogonal functions and intertwining operators, of category O for the rational Cherednik algebra of type G(r,p,n). As a first application, we give a…
Explicit expressions are proven for derivatives of the ratio of a determinant or Pfaffian determinant and a Vandermonde determinant. Such ratios appear for example in general group integrals of Harish-Chandra--Itzykson--Zuber type and in…
We study semantic and syntactic properties of spherical orders and their elementary theories, including finite and dense orders and their theories. It is shown that theories of dense $n$-spherical orders are countably categorical and…
We explore various combinatorial problems mostly borrowed from physics, that share the property of being continuously or discretely integrable, a feature that guarantees the existence of conservation laws that often make the problems…
We present a short analytic proof of the equality between the analytic and combinatorial torsion. We use the same approach as in the proof given by Burghelea, Friedlander and Kappeler, but avoid using the difficult Mayer-Vietoris type…
The problem of writing real zero polynomials as determinants of linear matrix polynomials has recently attracted a lot of attention. Helton and Vinnikov have proved that any real zero polynomial in two variables has a determinantal…