Reduced words for clans

2018/06/13 by Burks, Brian, Pawlowski, Brendan
#05A05 #05E05 #06A07 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1806.05247

Abstract

Clans are combinatorial objects indexing the orbits of GL(ℂ^p) × GL(ℂ^q) on the variety of flags in ℂ^p+q. This geometry leads to a partial order on the set of clans analogous to weak Bruhat order on the symmetric group, and we study the saturated chains in this order. We prove an analogue of the Matsumoto-Tits theorem on reduced words in a Coxeter group. We also obtain enumerations of reduced word sets for particular clans in terms of standard tableaux and shifted standard tableaux.

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• Sorting and generating reduced words
• Bumpless Pipe Dream Fragments -- Equivariant Geometry of Clans
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• Enumeration of Gelfand-Cetlin type reduced words