Related papers: On the problem of M-hyperquasivarieties

These notes are an expanded version of a talk given by the second author. Our main interest is focused on the challenging problem of computing Kronecker coefficients. We decided, at the beginning, to take a very general approach to the…

Based on the work of A. Vershik, we introduce two new combinatorial identities. We show how these identities can be used to prove a new hook-content identity. The main motivation for deriving this identity was a particular optimization…

In 2001 Thunder gave an estimate for the number of integer solutions of decomposable form inequalities under the assumption that the forms are of finite type. The purpose of this article is to generalize this result to forms which are of…

This paper is concerned with existence of a $C^{\alpha}$ viscosity solution of a second order non-translation invariant integro-PDE. We first obtain a weak Harnack inequality for such integro-PDE. We then use the weak Harnack inequality to…

This is a sequel to the author's book "Derived Langlands" which introduced an embedding of the category of admissible representations of a locally p-adic group in to the derived category of the monomial category of the group. This article…

We consider semigroup algorithmic problems in the wreath product $\mathbb{Z} \wr \mathbb{Z}$. Our paper focuses on two decision problems introduced by Choffrut and Karhum\"{a}ki (2005): the Identity Problem (does a semigroup contain the…

We prove the symmetry of solutions to overdetermined problems for a class of fully nonlinear equations, namely Hessian quotient equations and Hessian quotient curvature equations. Our approach is based on establishing a Rellich-Pohozaev…

Motivated by the works of Shiromoto [3] and Shi et al. [4], we study the existence of MacWilliams type identities with respect to Lee and Euclidean weight enumerators for linear codes over $\mathbb{Z}_{\ell}.$ Necessary and sufficient…

This is an expository article. We survey some fundamental trends in representation theory of symmetric groups and related objects which became apparent in the last fifteen years. The emphasis is on connections with Lie theory via…

The main result of [HL] (Annals of Math. 102 (1975), 223--290) gives a characterization of the boundaries of complex subvarieties in C^n. An application of this result concerning pseudoconvexity, namely Theorem 10.4 in [HL], is amplified.

Building upon the classical article "Representing varieties of algebras by algebras'' by W. D. Neumann, we revisit the famous Birkhoff's HSP theorem in the light of infinitary algebra.

In this paper, we prove a new identity for values of the Hurwitz zeta function which contains as particular cases Koecher's identity for odd zeta values, the Bailey-Borwein-Bradley identity for even zeta values and many other interesting…

Alon and F\"uredi (European J. Combin. 1993) gave a tight bound for the following hyperplane covering problem: find the minimum number of hyperplanes required to cover all points of the n-dimensional hypercube {0,1}^n except the origin.…

We study the problem of universal quantum cloning -- taking several identical copies of a pure but unknown quantum state and producing further copies. While it is well known that it is impossible to perfectly reproduce the state, how well…

We derive a simple lower bound for the multi-version coding problem formulated in [1]. We also propose simple algorithms that almost match the lower bound derived. Another lower bound is proven for an extended version of the multi-version…

We prove denominator identities for the periplectic Lie superalgebra $\mathfrak{p}(n)$, thereby completing the problem of finding denominator identities for all simple classical finite-dimensional Lie superalgebras.

We study the complexity of the computational task ``Given a colouring $c : \mathbb{Q} \to \mathbf{k}$, find a monochromatic $S \subseteq \mathbb{Q}$ such that $(S,<) \cong (\mathbb{Q},<)$''. The framework is Weihrauch reducibility. Our…

This paper gives bijective proofs of some novel coinversion identities first discovered by Ayyer, Mandelshtam, and Martin (arxiv:2011.06117) as part of their proof of a new combinatorial formula for the modified Macdonald polynomials…

We consider the Lane-Emden equation with a supercritical nonlinearity with an inhomogeneous Dirichlet boundary condition on an infinite cone. Under suitable conditions for the boundary data and the exponent of nonlinearity, we give a…

In this note, we prove the profile decomposition for hyperbolic Schr\"odinger (or mixed signature) equations on $\mathbb{R}^2$ in two cases, one mass-supercritical and one mass-critical. First, as a warm up, we show that the profile…