Alternating permutations and the mth descents

Kaǧan Kuruşngöz; Ae Ja Yee

doi:10.1016/j.disc.2011.08.005

Alternating permutations and the mth descents

Kaǧan Kuruşngöz, Ae Ja Yee

Mathematics

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

3 Scopus citations

Abstract

A half-descent of an alternating permutation π is an event that π2_i>π2_i+2, which is defined and studied in Huber and Yee (2010) [18]. The notion of half-descents is generalized to mth descents. Bivariate generating functions for permutations classified according to the numbers of mth descents and inversions are given. Connections to the results on half-descents and alternating permutations are indicated. It is also shown how to specialize the presented results to obtain some other previous work on permutations.

Original language	English (US)
Pages (from-to)	2610-2622
Number of pages	13
Journal	Discrete Mathematics
Volume	311
Issue number	22
DOIs	https://doi.org/10.1016/j.disc.2011.08.005
State	Published - Nov 28 2011

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/j.disc.2011.08.005

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title = "Alternating permutations and the mth descents",

abstract = "A half-descent of an alternating permutation π is an event that π2i>π2i+2, which is defined and studied in Huber and Yee (2010) [18]. The notion of half-descents is generalized to mth descents. Bivariate generating functions for permutations classified according to the numbers of mth descents and inversions are given. Connections to the results on half-descents and alternating permutations are indicated. It is also shown how to specialize the presented results to obtain some other previous work on permutations.",

author = "Kaǧan Kuru{\c s}ng{\"o}z and Yee, {Ae Ja}",

note = "Funding Information: The second author is partially supported by National Science Foundation Grant DMS-0801184 and by National Security Agency Grant H98230-10-1-0205 . ",

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AU - Kuruşngöz, Kaǧan

AU - Yee, Ae Ja

N1 - Funding Information: The second author is partially supported by National Science Foundation Grant DMS-0801184 and by National Security Agency Grant H98230-10-1-0205 .

PY - 2011/11/28

Y1 - 2011/11/28

N2 - A half-descent of an alternating permutation π is an event that π2i>π2i+2, which is defined and studied in Huber and Yee (2010) [18]. The notion of half-descents is generalized to mth descents. Bivariate generating functions for permutations classified according to the numbers of mth descents and inversions are given. Connections to the results on half-descents and alternating permutations are indicated. It is also shown how to specialize the presented results to obtain some other previous work on permutations.

AB - A half-descent of an alternating permutation π is an event that π2i>π2i+2, which is defined and studied in Huber and Yee (2010) [18]. The notion of half-descents is generalized to mth descents. Bivariate generating functions for permutations classified according to the numbers of mth descents and inversions are given. Connections to the results on half-descents and alternating permutations are indicated. It is also shown how to specialize the presented results to obtain some other previous work on permutations.

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Alternating permutations and the mth descents

Abstract

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