Existence of symmetric maximal noncrossing collections of k-element sets

2018/08/10 by Pasquali, Andrea, Thörnblad, Erik, Zimmermann, Jakob · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1808.03556

Abstract

We investigate the existence of maximal collections of mutually noncrossing k-element subsets of \ 1, …, n \ that are invariant under adding k\pmod n to all indices. Our main result is that such a collection exists if and only if k is congruent to 0, 1 or -1 modulo n/GCD(k,n). Moreover, we present some algebraic consequences of our result related to self-injective Jacobian algebras.

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