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On the positivity of the number of t-core partitions

Ken Ono (1994)

Acta Arithmetica

A partition of a positive integer n is a nonincreasing sequence of positive integers with sum n . Here we define a special class of partitions. 1. Let t 1 be a positive integer. Any partition of n whose Ferrers graph have no hook numbers divisible by t is known as a t- core partitionof n . The hooks are important in the representation theory of finite symmetric groups and the theory of cranks associated with Ramanujan’s congruences for the ordinary partition function [3, 4, 6]. If t 1 and n 0 , then we define...

On Thom Polynomials for A4(−) via Schur Functions

Öztürk, Özer (2007)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 05E05, 14N10, 57R45.We study the structure of the Thom polynomials for A4(−) singularities. We analyze the Schur function expansions of these polynomials. We show that partitions indexing the Schur function expansions of Thom polynomials for A4(−) singularities have at most four parts. We simplify the system of equations that determines these polynomials and give a recursive description of Thom polynomials for A4(−) singularities. We also give Thom polynomials...

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