Note on 1-crossing partitions

M. Bergerson, A. Miller, A. Pliml, Victor S Reiner, P. Shearer, Dennis W Stanton, N. Switala

Research output: Contribution to journalArticlepeer-review


It is shown that there are (2n-r-1 n-r) noncrossing partitions of an n-set together with a distinguished block of size r, and ( nk-1)(n-r-1k-2) of these have k blocks, generalizing a result of Bóna on partitions with one crossing. Furthermore, specializing natural q-analogues of these formulae with q equal to certain dth roots-of-unity gives the number of such objects having d-fold rotational symmetry.

Original languageEnglish (US)
Pages (from-to)83-87
Number of pages5
JournalArs Combinatoria
StatePublished - Apr 2011


  • Cyclic sieving phenonomenon
  • Noncrossing partition


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