Related papers: Generating functions for ranks of pre-modular cate…
We investigate the roots of Hilbert quasipolynomials arising from certain rational generating functions.
For a complex quasi-projective manifold with a finite group action, we define higher order generalized Euler characteristics with values in the Grothendieck ring of complex quasi-projective varieties extended by the rational powers of the…
We characterize, up to a conjecture, probability distributions of all order finite moments having ultraspherical type generating functions for orthogonal polynomials.
This paper concerns the enumeration of isomorphism classes of modules of a polynomial algebra in several variables over a finite field. This is the same as the classification of commuting tuples of matrices over a finite field up to…
A spectral factorization theorem is proved for polynomial rank-deficient matrix-functions. The theorem is used to construct paraunitary matrix-functions with first rows given.
In this paper we study substitutions and some of their associated generating functions. This association takes aperiodicity to transcendence, and vice-versa. These generating functions have a recursive structure arising from the…
We obtain q-analogues of the Sylvester, Ces\`aro, Pasternack, and Bateman polynomials. We also derive generating functions for these polynomials.
We explain how, under some hypotheses, one can construct a sequence of finite dimensional $kG$-modules that lie in certain prescribed additive subcategories, but whose direct limits do not. We use these to show that many of the triangulated…
We construct generators for modules of vector-valued Picard modular forms on a unitary group of type (2,1) over the Eisenstein integers. We also calculate eigenvalues of Hecke operators acting on cusp forms.
Let $c_n$ denote the number of nodes at a distance $n$ from the root of a rooted tree. A criterion for proving the rationality and computing the rational generating function of the sequence $\{c_n\}$ is described. This criterion is applied…
We discuss a method for computing the generating function for the multiplicity distribution in field theories with strong time dependent external sources. At leading order, the computation of the generating function reduces to finding a…
We thoroughly treat several familiar and less familiar definitions and results concerning categories, functors and distributors enriched in a base quantaloid Q. In analogy with V-category theory we discuss such things as adjoint functors,…
A generating function for the Wigner's $D$-matrix elements of $SU(3)$ is derived. From this an explicit expression for the individual matrix elements is obtained in a closed form.
We complete the classification of quantum subgroups of $SL_q(2)$ with $q$ a root of unity of arbitrary order, that is, Hopf algebra quotients of the quantum function algebras $\mathcal{O}_{q} (SL_2(\mathbb{C}))$.
We construct all integral non-group-theoretical modular categories of dimension $p^2q^2$, where $p$ and $q$ are distinct prime numbers, establishing that a necessary and sufficient condition for their existence is that $p \mid q+1$, and…
Categories are coreflectively embedded in multicategories via the "discrete cocone" construction, the right adjoint being given by the monoid construction. Furthermore, the adjunction lifts to the "cartesian level": preadditive categories…
We present a modular function-based approach to explaining, for primes larger than 3, the exponents that appear in the prime decomposition of the order of the monster finite simple group.
We consider the finite generation property for cohomology algebra of pointed finite tensor categories via de-equivariantization and exact sequence of finite tensor categories. As a result, we prove that all coradically graded pointed finite…
Mobiles are a particular class of decorated plane trees which serve as codings for planar maps. Here we address the question of enumerating mobiles in their most general flavor, in correspondence with planar Eulerian (i.e., bicolored) maps.…
It is shown that, in the 1-jet space of the circle, the swapping and the flyping procedures, which produce topologically equivalent links, can produce nonequivalent legendrian links. Each component of the links considered is legendrian…