Related papers: A Combination Theorem for PD(n)-Pairs
In recent work, G. E. Andrews and G. Simay prove a surprising relation involving parity palindromic compositions, and ask whether a combinatorial proof can be found. We extend their results to a more general class of compositions that are…
We prove a general duality theorem for tangle-like dense objects in combinatorial structures such as graphs and matroids. This paper continues, and assumes familiarity with, the theory developed in [6]
We prove a binomial formula for Macdonald polynomials and consider applications of it.
In this note, we give an alternate proof of the multinomial theorem using a probabilistic approach. Although the multinomial theorem is basically a combinatorial result, our proof may be simpler for a student familiar with only basic…
In this work we state a Theorem on number theory and apply it to solve some ordinary and partial differential equations.
We give a purely combinatorial proof for the infinitary van der Waerden's theorem.
We give a new simpler proof of a theorem of Jayne and Rogers.
A Lax pair for the 2D Euler equation is found.
We prove that the non-vanishing conjecture holds for generalized lc pairs with a polarization.
In this paper we show an index theorem for gerbes
In this paper, we introduce a new type of coupled fixed point theorem in partially ordered complete metric space. We give an example to support of our result.
We prove the special termination for log canonical pairs and its generalisation in the context of generalised pairs.
This article contains the proof of a theorem on orthogonal-Pin duality that was cited without proof in a previous article in this journal.
In 2017, E. Panzer proved the parity theorem for multiple polylogarithms. While his proof is simple and constructive, it does not yield a general explicit formula. Inspired by M. Hirose's recent work on the parity theorem for multiple zeta…
We prove the $\boldsymbol{p}$-adic duality theorem for the finite star-multiple polylogarithms. That is a generalization of Hoffman's duality theorem for the finite multiple zeta-star values.
We give a proof of the Thom-Sebastiani theorem for mixed Hodge modules using a compatibility with Verdier specialization.
We prove the complete intersection theorem and complete nontrivial-intersection theorem for systems of set partitions
We consider statistical procedures for hypothesis testing of real valued functionals of matched pairs with missing values. In order to improve the accuracy of existing methods, we propose a novel multiplication combination procedure.…
In this note we show that the known relation between double groupoids and matched pairs of groups may be extended, or seems to extend, to the triple case. The references give some other occurrences of double groupoids.
We generalize the optimal coupling theorem to multiple random variables: Given a collection of random variables, it is possible to couple all of them so that any two differ with probability comparable to the total-variation distance between…