Abstract:We study the poset of d-indivisible noncrossing partitions introduced by Mühle, Nadeau and Williams. These are noncrossing partitions such that each block and each dual block has cardinality~$1$ modulo $d$. Generalizing the work of Speicher, we introduce a generating function approach to reach new enumerative results and recover some known formulas on the cardinality, the Möbius function and the rank numbers. We compute the antipode of the Hopf algebra of d-indivisible noncrossing partition posets. Generalizing work of Stanley, we show that the bijection between the maximal chains and d-parking functions introduced by Mühle, Nadeau and Williams gives rise to an EL-labeling. Generalizing a construction of Yan, we also introduce d-parking trees which are in bijective correspondence with the maximal chains.
From: Richard Ehrenborg [view email]
[v1]
Thu, 11 Jul 2024 15:03:15 UTC (36 KB)
[v2]
Sun, 13 Oct 2024 20:13:04 UTC (33 KB)
[v3]
Fri, 4 Sep 2026 20:38:03 UTC (33 KB)
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