Classifying descents according to parity

Sergey Kitaev; Jeffrey Remmel

doi:10.1007/s00026-007-0313-2

Classifying descents according to parity

Sergey Kitaev, Jeffrey Remmel

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

12 Citations (Scopus)

Abstract

In this paper we refine the well-known permutation statistic “descent” by fixing parity of (exactly) one of the descent’s numbers. We provide explicit formulas for the distribution of these (four) new statistics. We use certain differential operators to obtain the formulas. Moreover, we discuss connection of our new statistics to the Genocchi numbers. We also provide bijective proofs of some of our results.

Original language	English
Pages (from-to)	173-193
Number of pages	21
Journal	Annals of Combinatorics
Volume	11
Issue number	2
DOIs	https://doi.org/10.1007/s00026-007-0313-2
Publication status	Published - 1 Aug 2007

Keywords

permutation statistics
descents
parity
bijection
combinatorics

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10.1007/s00026-007-0313-2

Cite this

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AU - Remmel, Jeffrey

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N2 - In this paper we refine the well-known permutation statistic “descent” by fixing parity of (exactly) one of the descent’s numbers. We provide explicit formulas for the distribution of these (four) new statistics. We use certain differential operators to obtain the formulas. Moreover, we discuss connection of our new statistics to the Genocchi numbers. We also provide bijective proofs of some of our results.

AB - In this paper we refine the well-known permutation statistic “descent” by fixing parity of (exactly) one of the descent’s numbers. We provide explicit formulas for the distribution of these (four) new statistics. We use certain differential operators to obtain the formulas. Moreover, we discuss connection of our new statistics to the Genocchi numbers. We also provide bijective proofs of some of our results.

KW - permutation statistics

KW - descents

KW - parity

KW - bijection

KW - combinatorics

UR - https://personal.cis.strath.ac.uk/sergey.kitaev/index_files/Papers/EOdescents.pdf

U2 - 10.1007/s00026-007-0313-2

DO - 10.1007/s00026-007-0313-2

M3 - Article

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VL - 11

SP - 173

EP - 193

JO - Annals of Combinatorics

JF - Annals of Combinatorics

IS - 2

ER -

Classifying descents according to parity

Abstract

Keywords

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