Classifying descents according to equivalence mod k

Sergey Kitaev, Jeffrey Remmel

Research output: Contribution to conferenceAbstract

7 Citations (Scopus)

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.
LanguageEnglish
Number of pages6
Publication statusPublished - 12 Jun 2006
EventPermutation Patterns Conference - Reykjavik University, Reykjavik, Iceland
Duration: 12 Jun 200616 Jun 2006

Conference

ConferencePermutation Patterns Conference
CountryIceland
CityReykjavik
Period12/06/0616/06/06

Fingerprint

Descent
Equivalence
Statistics
Permutation Statistics
Inclusion-exclusion
Bijective
Parity
Generalise

Keywords

  • classifying descents
  • permutation patterns
  • mod k

Cite this

Kitaev, S., & Remmel, J. (2006). Classifying descents according to equivalence mod k. Abstract from Permutation Patterns Conference , Reykjavik, Iceland.
Kitaev, Sergey ; Remmel, Jeffrey. / Classifying descents according to equivalence mod k. Abstract from Permutation Patterns Conference , Reykjavik, Iceland.6 p.
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Kitaev, S & Remmel, J 2006, 'Classifying descents according to equivalence mod k' Permutation Patterns Conference , Reykjavik, Iceland, 12/06/06 - 16/06/06, .

Classifying descents according to equivalence mod k. / Kitaev, Sergey; Remmel, Jeffrey.

2006. Abstract from Permutation Patterns Conference , Reykjavik, Iceland.

Research output: Contribution to conferenceAbstract

TY - CONF

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

ER -

Kitaev S, Remmel J. Classifying descents according to equivalence mod k. 2006. Abstract from Permutation Patterns Conference , Reykjavik, Iceland.