Enumeration formulas for young tableaux in a diagonal strip

Yuliy Baryshnikov, Dan Romik

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

We derive combinatorial identities, involving the Bernoulli and Euler numbers, for the numbers of standard Young tableaux of certain skew shapes. This generalizes the classical formulas of D. André on the number of up-down permutations. The analysis uses a transfer operator approach extending the method of Elkies, combined with an identity expressing the volume of a certain polytope in terms of a Schur function.

Original languageEnglish
Pages (from-to)157-186
Number of pages30
JournalIsrael Journal of Mathematics
Volume178
Issue number1
DOIs
Publication statusPublished - Dec 1 2010
Externally publishedYes

Fingerprint

Young Tableaux
Enumeration
Strip
Combinatorial Identities
Transfer Operator
Euler numbers
Bernoulli numbers
Schur Functions
Polytope
Skew
Permutation
Generalise
Standards

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Enumeration formulas for young tableaux in a diagonal strip. / Baryshnikov, Yuliy; Romik, Dan.

In: Israel Journal of Mathematics, Vol. 178, No. 1, 01.12.2010, p. 157-186.

Research output: Contribution to journalArticle

Baryshnikov, Yuliy ; Romik, Dan. / Enumeration formulas for young tableaux in a diagonal strip. In: Israel Journal of Mathematics. 2010 ; Vol. 178, No. 1. pp. 157-186.
@article{9a24080e697d41ae9c0e72f36a73d101,
title = "Enumeration formulas for young tableaux in a diagonal strip",
abstract = "We derive combinatorial identities, involving the Bernoulli and Euler numbers, for the numbers of standard Young tableaux of certain skew shapes. This generalizes the classical formulas of D. Andr{\'e} on the number of up-down permutations. The analysis uses a transfer operator approach extending the method of Elkies, combined with an identity expressing the volume of a certain polytope in terms of a Schur function.",
author = "Yuliy Baryshnikov and Dan Romik",
year = "2010",
month = "12",
day = "1",
doi = "10.1007/s11856-010-0061-6",
language = "English",
volume = "178",
pages = "157--186",
journal = "Israel Journal of Mathematics",
issn = "0021-2172",
publisher = "Springer New York",
number = "1",

}

TY - JOUR

T1 - Enumeration formulas for young tableaux in a diagonal strip

AU - Baryshnikov, Yuliy

AU - Romik, Dan

PY - 2010/12/1

Y1 - 2010/12/1

N2 - We derive combinatorial identities, involving the Bernoulli and Euler numbers, for the numbers of standard Young tableaux of certain skew shapes. This generalizes the classical formulas of D. André on the number of up-down permutations. The analysis uses a transfer operator approach extending the method of Elkies, combined with an identity expressing the volume of a certain polytope in terms of a Schur function.

AB - We derive combinatorial identities, involving the Bernoulli and Euler numbers, for the numbers of standard Young tableaux of certain skew shapes. This generalizes the classical formulas of D. André on the number of up-down permutations. The analysis uses a transfer operator approach extending the method of Elkies, combined with an identity expressing the volume of a certain polytope in terms of a Schur function.

UR - http://www.scopus.com/inward/record.url?scp=79251546446&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79251546446&partnerID=8YFLogxK

U2 - 10.1007/s11856-010-0061-6

DO - 10.1007/s11856-010-0061-6

M3 - Article

AN - SCOPUS:79251546446

VL - 178

SP - 157

EP - 186

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

SN - 0021-2172

IS - 1

ER -