Classifying descents according to equivalence mod k

Sergey Kitaev; Jeffrey Remmel

Abstract

In [5] the authors re¯ne the well-known permutation statistic \descent" by ¯xing parity of one of the descent's numbers. In this paper, we generalize the results of [5] by studying descents according to whether the ¯rst or the second element in a descent pair is equivalent to k mod k ¸ 2. We provide either an explicit or an inclusion-exclusion type formula for the distribution of the new statistics. Based on our results we obtain combinatorial proofs of a number of remarkable identities. We also provide bijective proofs of some of our results.

Original language	English
Number of pages	6
Publication status	Published - 12 Jun 2006
Event	Permutation Patterns Conference - Reykjavik University, Reykjavik, Iceland Duration: 12 Jun 2006 → 16 Jun 2006

Conference

Conference	Permutation Patterns Conference
Country/Territory	Iceland
City	Reykjavik
Period	12/06/06 → 16/06/06

Keywords

classifying descents
permutation patterns
mod k

Cite this

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title = "Classifying descents according to equivalence mod k",

abstract = "In [5] the authors re¯ne the well-known permutation statistic \textbackslash{}descent{"} by ¯xing parity of one of the descent's numbers. In this paper, we generalize the results of [5] by studying descents according to whether the ¯rst or the second element in a descent pair is equivalent to k mod k ¸ 2. We provide either an explicit or an inclusion-exclusion type formula for the distribution of the new statistics. Based on our results we obtain combinatorial proofs of a number of remarkable identities. We also provide bijective proofs of some of our results.",

keywords = "classifying descents, permutation patterns, mod k",

author = "Sergey Kitaev and Jeffrey Remmel",

year = "2006",

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day = "12",

language = "English",

note = "Permutation Patterns Conference ; Conference date: 12-06-2006 Through 16-06-2006",

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T1 - Classifying descents according to equivalence mod k

AU - Kitaev, Sergey

AU - Remmel, Jeffrey

PY - 2006/6/12

Y1 - 2006/6/12

N2 - In [5] the authors re¯ne the well-known permutation statistic \descent" by ¯xing parity of one of the descent's numbers. In this paper, we generalize the results of [5] by studying descents according to whether the ¯rst or the second element in a descent pair is equivalent to k mod k ¸ 2. We provide either an explicit or an inclusion-exclusion type formula for the distribution of the new statistics. Based on our results we obtain combinatorial proofs of a number of remarkable identities. We also provide bijective proofs of some of our results.

AB - In [5] the authors re¯ne the well-known permutation statistic \descent" by ¯xing parity of one of the descent's numbers. In this paper, we generalize the results of [5] by studying descents according to whether the ¯rst or the second element in a descent pair is equivalent to k mod k ¸ 2. We provide either an explicit or an inclusion-exclusion type formula for the distribution of the new statistics. Based on our results we obtain combinatorial proofs of a number of remarkable identities. We also provide bijective proofs of some of our results.

KW - classifying descents

KW - permutation patterns

KW - mod k

UR - http://www.cs.otago.ac.nz/staffpriv/mike/PP2006/Programme.html

M3 - Abstract

T2 - Permutation Patterns Conference

Y2 - 12 June 2006 through 16 June 2006

ER -

Classifying descents according to equivalence mod k

Abstract

Conference

Keywords

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Cite this