The rook monoid is lexicographically shellable

Can, Mahir Bilen

doi:10.1016/j.ejc.2019.05.009

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Cited by 8 publications

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“…This poset structure on R n is well studied, [4]. It is known that (R n , ≤) is a graded, bounded, EL-shellable poset, see [3]. Towards a proof of Theorem 1, we make use of an important algebraic submonoid of Mat n ; it is the closure in Zariski topology of the Borel subgroup B n in Mat n .…”

Section: Introductionmentioning

confidence: 99%

Stirling Posets

Can,

Cherniavsky

2018

Preprint

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We define combinatorially a partial order on the set partitions and show that it is equivalent to the Bruhat-Chevalley-Renner order on the upper triangular matrices. By considering subposets consisting of set partitions with a fixed number of blocks, we introduce and investigate "Stirling posets." As we show, the Stirling posets have a hierarchy and they glue together to give the whole set partition poset. Moreover, we show that they (Stirling posets) are graded and EL-shellable. We offer various reformulations of their length functions and determine the recurrences for their length generating series.

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Section: Introductionmentioning

confidence: 99%