We investigate two classes of multivariate polynomials with variables indexed by the edges a uniform hypergraph and coefficients depending on certain patterns unions edges. These arise naturally to model job-occupancy in some queuing problems redundancy scheduling policies. The question, posed Cardinaels, Borst, van Leeuwaarden [Redundancy Scheduling Locally Stable Compatibility Graphs, arXiv p...

We introduce a class of orthogonal polynomials in two variables which generalizes the disc polynomials and the 2-D Hermite polynomials. We identify certain interesting members of this class including a one variable generalization of the 2-D Hermite polynomials and a two variable extension of the Zernike or disc polynomials. We also give q-analogues of all these extensions. In each case in addit...

We consider Takahashi’s categorical interpretation of the Berglund–Hubsch mirror symmetry conjecture for invertible polynomials in case chain polynomials. Our strategy is based on a stronger claim that relevant categories satisfy recursion directed $$A_{\infty }$$ -categories, which may be independent interest. give full proof this B-side. On A-side we detailed sketch an argument, falls short b...

Landau-Ginzburg mirror symmetry studies isomorphisms between graded Frobenius algebras, known as Aand B-models. Fundamental to constructing these models is the computation of the finite, Abelian maximal symmetry group Gmax W of a given polynomial W . For invertible polynomials, which have the same number of monomials as variables, a generating set for this group can be computed efficiently by i...

The main purpose of this paper is to introduce and investigate a new class of generalized Bernoulli polynomials and Euler polynomials based on the q-integers. The q-analogues of well-known formulas are derived. The q-analogue of the Srivastava–Pintér addition theorem is obtained. We give new identities involving q-Bernstein polynomials.

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract In this paper, we give a new symmetry identities for the generalized higher-order (h, q)-Bernoulli polynomials which are derive from the properties of symmetry of Volkenborn...