Block numbers of permutations and Schur-positivity

Ron Adin; Yuval Roichman; Eli Bagno

Block numbers of permutations and Schur-positivity

Ron Adin
, Yuval Roichman
, Eli Bagno

Department of Mathematics

Jerusalem College of Technology

Research output: Contribution to journal › Conference article › peer-review

Abstract

The block number of a permutation is the maximal number of components in its expression as a direct sum. We show that the distribution of the set of left-toright-maxima over 321-avoiding permutations with a given block number k is equal
to the distribution of this set over 321-avoiding permutations with the last descent of the inverse permutation at position n − k. This result is analogous to the FoataSchützenberger equi-distribution theorem, and implies Schur-positivity of the quasisymmetric generating function of descent set over 321-avoiding permutations with a prescribed block number

Original language	American English
Article number	64
Number of pages	12
Journal	Seminaire Lotharingien de Combinatoire
Volume	78B
State	Published - 2017

Bibliographical note

Proceedings of the 29th Conference on Formal Power
Article #64, 12 pp. Series and Algebraic Combinatorics (London)

Keywords

Schur positivity
permutation statistics
Pattern avoidance
quasi-symmetric function

Cite this

@article{60c856fbef374c729c4f41b2820ae1e3,

title = "Block numbers of permutations and Schur-positivity",

abstract = "The block number of a permutation is the maximal number of components in its expression as a direct sum. We show that the distribution of the set of left-toright-maxima over 321-avoiding permutations with a given block number k is equal to the distribution of this set over 321-avoiding permutations with the last descent of the inverse permutation at position n − k. This result is analogous to the FoataSch{\"u}tzenberger equi-distribution theorem, and implies Schur-positivity of the quasisymmetric generating function of descent set over 321-avoiding permutations with a prescribed block number",

keywords = "Schur positivity, permutation statistics, Pattern avoidance, quasi-symmetric function",

author = "Ron Adin and Yuval Roichman and Eli Bagno",

note = "Proceedings of the 29th Conference on Formal Power Article \#64, 12 pp. Series and Algebraic Combinatorics (London)",

year = "2017",

language = "American English",

volume = "78B",

journal = "Seminaire Lotharingien de Combinatoire",

}

TY - JOUR

T1 - Block numbers of permutations and Schur-positivity

AU - Adin, Ron

AU - Roichman, Yuval

AU - Bagno, Eli

N1 - Proceedings of the 29th Conference on Formal Power Article #64, 12 pp. Series and Algebraic Combinatorics (London)

PY - 2017

Y1 - 2017

N2 - The block number of a permutation is the maximal number of components in its expression as a direct sum. We show that the distribution of the set of left-toright-maxima over 321-avoiding permutations with a given block number k is equal to the distribution of this set over 321-avoiding permutations with the last descent of the inverse permutation at position n − k. This result is analogous to the FoataSchützenberger equi-distribution theorem, and implies Schur-positivity of the quasisymmetric generating function of descent set over 321-avoiding permutations with a prescribed block number

AB - The block number of a permutation is the maximal number of components in its expression as a direct sum. We show that the distribution of the set of left-toright-maxima over 321-avoiding permutations with a given block number k is equal to the distribution of this set over 321-avoiding permutations with the last descent of the inverse permutation at position n − k. This result is analogous to the FoataSchützenberger equi-distribution theorem, and implies Schur-positivity of the quasisymmetric generating function of descent set over 321-avoiding permutations with a prescribed block number

KW - Schur positivity

KW - permutation statistics

KW - Pattern avoidance

KW - quasi-symmetric function

UR - https://scholar.google.com/scholar?hl=en&as_sdt=0%2C5&q=Block+numbers+of+permutations+and+Schur-positivity&btnG=

M3 - Conference article

VL - 78B

JO - Seminaire Lotharingien de Combinatoire

JF - Seminaire Lotharingien de Combinatoire

M1 - 64

ER -

Block numbers of permutations and Schur-positivity

Abstract

Bibliographical note

Keywords

Other files and links

Fingerprint

Cite this