Stirling posets

Mahir Bilen Can, Yonah Cherniavsky

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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.

Original languageEnglish
Pages (from-to)185-219
Number of pages35
JournalIsrael Journal of Mathematics
Issue number1
StatePublished - 1 Mar 2020


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