Related papers: Generating functions for tensor products

A recursive method is given for finding generating functions which enumerate rooted hypermaps by number of vertices, edges and faces for any given number of darts. It makes use of matrix-integral expressions arising from the study of…

In this paper, we revisit the application of generating trees to the pattern avoidance problem for permutations. In particular, we study this problem for certain general sets of patterns and propose a new procedure leveraging the FinLabel…

A general explicit form for generating functions for approximating fractional derivatives is derived. To achieve this, an equivalent characterisation for consistency and order of approximations established on a general generating function…

A novel combinatorial formula is developed for for tensor product multiplicities in representation theory. We introduce a difference formula linking these multiplicities to restricted occupancy coefficients via a shifted operator. This…

The fact that Schubert polynomials are the weighted counting functions for reduced RC-graphs, also known as reduced pipe dreams, was established using their generating functions inside an appropriate Demazure algebra. Here we investigate…

We consider the problem of learning mixtures of generalized linear models (GLM) which arise in classification and regression problems. Typical learning approaches such as expectation maximization (EM) or variational Bayes can get stuck in…

Groups preserving a distributive product are encountered often in algebra. Examples include automorphism groups of associative and nonassociative rings, classical groups, and automorphism groups of p-groups. While the great variety of such…

We develop methods of computation of the Brauer-Picard groups of fusion categories and apply them to compute such groups for several classes of fusion categories of prime power dimension: representation categories of elementary abelian…

We give universal upper bounds on the relative dimensions of isotypic components of a tensor product of the linear group GL(n) representations and universal upper bounds on the relative dimensions of irreducible components of a tensor…

We show how Andrews' generating functions for generalized Frobenius partitions can be understood within the theory of Eichler and Zagier as specific coefficients of certain Jacobi forms. This reformulation leads to a recursive process which…

This paper explores the possibility of constructing multivariate generating functions for all cohomology dimensions of all holomorphic line bundles on certain complex projective varieties of Fano, Calabi-Yau and general type in various…

In this paper we study the tensor product of two $f$-algebras. We show that the Riesz Subspace generated by a subalgebra in an $f$-algebra is an algebra in order to prove that the Riesz tensor product of two $f$-algebras has a structure of…

Using the notion of multivariate lower set interpolation, we construct nodal basis functions for the serendipity family of finite elements, of any order and any dimension. For the purpose of computation, we also show how to express these…

We investigate the problem of computing tensor product multiplicities for complex semisimple Lie algebras. Even though computing these numbers is #P-hard in general, we show that if the rank of the Lie algebra is assumed fixed, then there…

We compute generating functions for the sum of the real-valued character degrees of the finite general linear and unitary groups, through symmetric function computations. For the finite general linear group, we get a new combinatorial proof…

We introduce a generating function approach to the affine Brauer and Kauffman categories and show how it allows one to efficiently recover important sets of relations in these categories. We use this formalism to deduce restrictions on…

This paper presents a novel approach to constructing finite generating sets for infinitely generated ideals. By integrating algebraic and computational techniques, we provide a method to identify finite generators, demonstrated through…

We consider sequences of integers defined by a system of linear inequalities with integer coefficients. We show that when the constraints are strong enough to guarantee that all the entries are nonnegative, the generating function for the…

We describe a general approach to obtain the generating functions of the characters of simple Lie algebras which is based on the theory of the quantum trigonometric Calogero-Sutherland model. We show how the method works in practice by…

The Steinberg tensor product theorem is a fundamental result in the modular representation theory of reductive algebraic groups. It describes any finite-dimensional simple module of highest weight $\lambda$ over such a group as the tensor…