In a recent paper, [2], Gill, using methods of the modular representation theory of finite groups, describes some results on the tensor product of Young modules for symmetric groups. We here give an alternative approach using the polynomial representation theory of general linear groups and the Schur functor. The main result is a formula for the multiplicities of Young modules in a tensor produ...

We prove upper bounds on the order and degree of the polynomials involved in a resolvent representation of the prime differential ideal associated with a polynomial differential system for a particular class of ordinary first order algebraic-differential equations arising in control theory. We also exhibit a probabilistic algorithm which computes this resolvent representation within time polyno...

Multivariate polynomial interpolation plays a crucial role both in scientific computation and engineering application. Exploring the structure of D-invariant (closed under differentiation) subspaces has significant meaning for multivariate Hermite-type (especially ideal interpolation). We analyze subspace Pn terms Cartesian tensors, where is with maximal total degree equal to n,n≥1. For an arbi...

A series representation for the Riemann zeta function in terms of the falling Pochhammer symbol is derived from the polynomial representation of the GaussKuzmin-Wirsing (GKW) operator.

This paper presents a descriptor representation-based guaranteed cost design methodology for polynomial fuzzy systems. applies the representation presenting closed-loop system of model with parallel distributed compensation (PDC) based controller. By utility representation, control (GCC) analysis can utilize slack matrices obtaining less conservative results. The proposed GCC is presented as su...

A new “polynomial sieve” is presented and used to show that almost all integers have at most one representation as a sum of two values of a given polynomial of degree at least 3.

Action-Graph Games (AGGs) are a fully expressive game representation which can compactly express strict and context-specific independence and anonymity structure in players’ utility functions. We present an efficient algorithm for computing expected payoffs under mixed strategy profiles. This algorithm runs in time polynomial in the size of the AGG representation (which is itself polynomial in ...