21 citations · 136 across the 32 of their papers we have counts for
11 papers · 1 filter
Minimal partitions with a given -core and -core
Matthew Fayers
Suppose and are coprime positive integers, and let be an -core partition and a -core partition. In this paper we consider the set of par…
A note on Kostka numbers
Matthew Fayers
We give an elementary proof of a well-known result on Kostka numbers, following a question from Mark Wildon on MathOverflow. Namely, we show that given partitions of wi…
2-chains: an interesting family of posets
Matthew Fayers
We introduce a new family of finite posets which we call 2-chains. These first arose in the study of 0-Hecke algebras, but they admit a variety of different characterisations. We g…
Simultaneous core multipartitions
Matthew Fayers
We initiate the study of simultaneous core multipartitions, generalising simultaneous core partitions, which have been studied extensively in the recent literature. Given a multipa…
-cores: a weighted version of Armstrong's conjecture
Matthew Fayers
The study of core partitions has been very active in recent years, with the study of -cores - partitions which are both - and -cores - playing a prominent role. A conj…
Dyck tilings and the homogeneous Garnir relations for graded Specht modules
Matthew Fayers
Suppose and are integer partitions with . Kenyon and Wilson have introduced the notion of a cover-inclusive Dyck tiling of the skew Young diagram …