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math.RT2009
Vertices of Specht modules and blocks of the symmetric group
Mark Wildon
This paper studies the vertices, in the sense defined by J. A. Green, of Specht modules for symmetric groups. The main theorem gives, for each indecomposable non-projective Specht…
math.CO2009
Knights, spies, games and ballot sequences
Mark Wildon
This paper presents a solution to the Knights and Spies Problem: In a room there are n people, each labelled with a unique number between 1 and n. A person may either be a knight o…
math.RT2009
Multiplicity-free representations of symmetric groups
Mark Wildon
Building on work of Saxl, we classify the multiplicity-free permutation characters of all symmetric groups of degree 66 or more. A corollary is a complete list of the irreducible c…