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- W4300695250 abstract "For coprime positive integers $a<b$, Armstrong, Rhoades, and Williams (2013) defined a set $NC(a,b)$ of rational noncrossing partitions, a subset of the ordinary noncrossing partitions of ${1, ldots, b-1}$. Bodnar and Rhoades (2015) confirmed their conjecture that $NC(a,b)$ is closed under rotation and proved an instance of the cyclic sieving phenomenon for this rotation action. We give a definition of $NC(a,b)$ which works for all coprime $a$ and $b$ and prove closure under rotation and cyclic sieving in this more general setting. We also generalize noncrossing parking functions to all coprime $a$ and $b$, and provide a character formula for the action of $mathfrak{S}_a times mathbb{Z}_{b-1}$ on $mathsf{Park}^{NC}(a,b)$." @default.
- W4300695250 created "2022-10-04" @default.
- W4300695250 creator A5066005176 @default.
- W4300695250 date "2017-01-25" @default.
- W4300695250 modified "2023-09-27" @default.
- W4300695250 title "Rational Noncrossing Partitions for all Coprime Pairs" @default.
- W4300695250 doi "https://doi.org/10.48550/arxiv.1701.07198" @default.
- W4300695250 hasPublicationYear "2017" @default.
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