Existence of symmetric maximal noncrossing collections of $k$-element sets
| Autor: | Pasquali, Andrea, Thörnblad, Erik, Zimmermann, Jakob |
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| Rok vydání: | 2018 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We investigate the existence of maximal collections of mutually noncrossing $k$-element subsets of $\left\{ 1, \dots, n \right\}$ 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 $n/\operatorname{GCD}(k,n)$. Moreover, we present some algebraic consequences of our result related to self-injective Jacobian algebras. Comment: 12 pages, 1 figure. Final version, to appear in Journal of Algebraic Combinatorics |
| Databáze: | arXiv |
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