Generators of supersymmetric polynomials in positive characteristic

Finding Characteristic Polynomials for LFSMs Used as Test Pattern Generators

– A built–in Test Pattern Generation (TPG) mechanism that is very popular for pseudorandom or pseudo–exhaustive TPG is a shift register whose initial portion is configured as a Linear Feedback Shift Register (LFSR), or some other kind of a Linear Finite State Machine (LFSM). A fundamental problem that exists in this mechanism is the presence of linear dependencies among the bit sequences produc...

Kangaroo Points and Oblique Polynomials in Resolution of Positive Characteristic

In September 2008, Heisuke Hironaka gave a series of lectures at the Clay Mathematics Institute explaining his program for the resolution of singularities in positive characteristic [Hi1]. In the course of the lectures, Hironaka relied on results of the author from an unpublished manuscript written in 2003 [Ha1]. The quoted results investigate the main obstruction for resolution in positive cha...

Exceptional polynomials and monodromy groups in positive characteristic

Contents 1. Introduction 1

Characteristic Polynomials

Introduction. Let F be a field and let V be a finite dimensional vector space over F which is also a module over the ring F[a]. Here a may lie in any extension ring of F. We do not assume, as yet, that V is a faithful module, so that a need not be a linear transformation on V. It is known that by means of a decomposition of V into cyclic F[a]-modules we may obtain a definition of the characteri...

Oscillation Properties of Generalized Characteristic Polynomials for Totally Positive and Positive Definite Matrices