Counting characters in linear group actions

On the Restriction of Characters of Special Linear Groups of Dimension Three

Linear-Space Substring Range Counting over Polylogarithmic Alphabets

Bille and Gørtz (2011) recently introduced the problem of substring range counting, for which we are asked to store compactly a string S of n characters with integer labels in [0, u], such that later, given an interval [a, b] and a pattern P of length m, we can quickly count the occurrences of P whose first characters’ labels are in [a, b]. They showed how to store S in O(n logn/ log logn) spac...

Ribbon Tile Invariants

Let T be a finite set of tiles, and B a set of regions Γ tileable by T. We introduce a tile counting group G(T,B) as a group of all linear relations for the number of times each tile τ ∈ T can occur in a tiling of a region Γ ∈ B. We compute the tile counting group for a large set of ribbon tiles, also known as rim hooks, in a context of representation theory of the symmetric group. The tile cou...

Finite Groups, Designs and Codes

Introduction Terminology and notation Group Actions and Permutation Characters Method 1 References Finite Groups, Designs and Codes J Moori School of Mathematical Sciences, University of KwaZulu-Natal Pietermaritzburg 3209, South Africa ASI, Opatija, 31 May –11 June 2010 J Moori, ASI 2010, Opatija, Croatia Groups, Designs and Codes Abstract Introduction Terminology and notation Group Actions an...

Dade’s Invariant Conjecture for General Linear and Unitary Groups in Non-defining Characteristics

This paper is part of a program to study the conjecture of E. C. Dade on counting characters in blocks for several finite groups. The invariant conjecture of Dade is proved for general linear and unitary groups when the characteristic of the modular representation is distinct from the defining characteristic of the groups.