# Dyck tilings and the homogeneous Garnir relations for graded Specht modules

@article{Fayers2013DyckTA,
title={Dyck tilings and the homogeneous Garnir relations for graded Specht modules},
author={Matthew Fayers},
journal={Journal of Algebraic Combinatorics},
year={2013},
volume={45},
pages={1041-1082}
}
• M. Fayers
• Published 25 September 2013
• Mathematics
• Journal of Algebraic Combinatorics
Suppose $$\lambda$$λ and $$\mu$$μ are integer partitions with $$\lambda \supseteq \mu$$λ⊇μ. Kenyon and Wilson have introduced the notion of a cover-inclusive Dyck tiling of the skew Young diagram $$\lambda \backslash \mu$$λ\μ, which has applications in the study of double-dimer models. We examine these tilings in more detail, giving various equivalent conditions and then proving a recurrence which we use to show that the entries of the transition matrix between two bases for a certain…
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Dyck tilings were introduced by Kenyon and Wilson in their study of double-dimer pairings. They are certain kinds of tilings of skew Young diagrams with ribbon tiles shaped like Dyck paths. We give
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