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Stirling posets

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Abstract

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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Authors and Affiliations

  1. Department of Mathematics, Tulane University, New Orleans, LA, 70118, USA

    Mahir Bilen Can

  2. Department of Mathematics, Ariel University, Kiryat Hamada, Ariel, 40700, USA

    Yonah Cherniavsky

Authors
  1. Mahir Bilen Can
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  2. Yonah Cherniavsky
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Correspondence to Mahir Bilen Can.

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Can, M.B., Cherniavsky, Y. Stirling posets. Isr. J. Math. 237, 185–219 (2020). https://doi.org/10.1007/s11856-020-2004-1

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  • DOI: https://doi.org/10.1007/s11856-020-2004-1

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