Note on 1-crossing partitions

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

Note on 1-crossing partitions

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

School of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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 ( ⁿ_k-1)(^n-r-1_k-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 d^th roots-of-unity gives the number of such objects having d-fold rotational symmetry.

Original language	English (US)
Pages (from-to)	83-87
Number of pages	5
Journal	Ars Combinatoria
Volume	99
State	Published - Apr 2011

Keywords

Cyclic sieving phenonomenon
Noncrossing partition

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title = "Note on 1-crossing partitions",

abstract = "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 B{\'o}na 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.",

keywords = "Cyclic sieving phenonomenon, Noncrossing partition",

author = "M. Bergerson and A. Miller and A. Pliml and Reiner, {Victor S} and P. Shearer and Stanton, {Dennis W} and N. Switala",

year = "2011",

month = apr,

language = "English (US)",

volume = "99",

pages = "83--87",

journal = "Ars Combinatoria",

issn = "0381-7032",

publisher = "Charles Babbage Research Centre",

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TY - JOUR

T1 - Note on 1-crossing partitions

AU - Bergerson, M.

AU - Miller, A.

AU - Pliml, A.

AU - Reiner, Victor S

AU - Shearer, P.

AU - Stanton, Dennis W

AU - Switala, N.

PY - 2011/4

Y1 - 2011/4

N2 - 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.

AB - 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.

KW - Cyclic sieving phenonomenon

KW - Noncrossing partition

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M3 - Article

AN - SCOPUS:79953844929

SN - 0381-7032

VL - 99

SP - 83

EP - 87

JO - Ars Combinatoria

JF - Ars Combinatoria

ER -

Note on 1-crossing partitions

Abstract

Keywords

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