The excedance algebra

Eric Clark; Richard Ehrenborg

doi:10.1016/j.disc.2013.03.014

The excedance algebra

Eric Clark
, Richard Ehrenborg

Mathematics

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

3 Scopus citations

Abstract

Motivated by the excedance set statistic, we define the excedance algebra as the quotient algebra k(a, b)/(ba - ab - a - b). We examine the expansion of any monomial in terms of the linear basis a^mbⁿ using alternating tableaux and shift invariant operators. As a result we obtain a new combinatorial interpretation of the coefficients of the Gandhi polynomials.

Original language	English
Pages (from-to)	1429-1435
Number of pages	7
Journal	Discrete Mathematics
Volume	313
Issue number	13
DOIs	https://doi.org/10.1016/j.disc.2013.03.014
State	Published - Jul 6 2013

Bibliographical note

Funding Information:
The authors would like to thank Carl Lee and Margaret Readdy for reading and commenting on an early version of this paper. The second author also thanks the Institute for Advanced Study where part of this research was done. The second author was partially supported by the National Science Foundation grants DMS-0902063 , DMS-0835373 , and CCF-0832797 .

Funding

The authors would like to thank Carl Lee and Margaret Readdy for reading and commenting on an early version of this paper. The second author also thanks the Institute for Advanced Study where part of this research was done. The second author was partially supported by the National Science Foundation grants DMS-0902063 , DMS-0835373 , and CCF-0832797 .

Funders	Funder number
National Science Foundation (NSF)	CCF-0832797, DMS-0902063, DMS-0835373

Keywords

Alternative tableaux
Excedance set statistic
Gandhi polynomials
Genocchi numbers
Operator identities

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/j.disc.2013.03.014

Cite this

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title = "The excedance algebra",

abstract = "Motivated by the excedance set statistic, we define the excedance algebra as the quotient algebra k(a, b)/(ba - ab - a - b). We examine the expansion of any monomial in terms of the linear basis ambn using alternating tableaux and shift invariant operators. As a result we obtain a new combinatorial interpretation of the coefficients of the Gandhi polynomials.",

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author = "Eric Clark and Richard Ehrenborg",

note = "Funding Information: The authors would like to thank Carl Lee and Margaret Readdy for reading and commenting on an early version of this paper. The second author also thanks the Institute for Advanced Study where part of this research was done. The second author was partially supported by the National Science Foundation grants DMS-0902063 , DMS-0835373 , and CCF-0832797 .",

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AU - Clark, Eric

AU - Ehrenborg, Richard

N1 - Funding Information: The authors would like to thank Carl Lee and Margaret Readdy for reading and commenting on an early version of this paper. The second author also thanks the Institute for Advanced Study where part of this research was done. The second author was partially supported by the National Science Foundation grants DMS-0902063 , DMS-0835373 , and CCF-0832797 .

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Y1 - 2013/7/6

N2 - Motivated by the excedance set statistic, we define the excedance algebra as the quotient algebra k(a, b)/(ba - ab - a - b). We examine the expansion of any monomial in terms of the linear basis ambn using alternating tableaux and shift invariant operators. As a result we obtain a new combinatorial interpretation of the coefficients of the Gandhi polynomials.

AB - Motivated by the excedance set statistic, we define the excedance algebra as the quotient algebra k(a, b)/(ba - ab - a - b). We examine the expansion of any monomial in terms of the linear basis ambn using alternating tableaux and shift invariant operators. As a result we obtain a new combinatorial interpretation of the coefficients of the Gandhi polynomials.

KW - Alternative tableaux

KW - Excedance set statistic

KW - Gandhi polynomials

KW - Genocchi numbers

KW - Operator identities

UR - https://www.scopus.com/pages/publications/84893709542

UR - https://www.scopus.com/pages/publications/84893709542#tab=citedBy

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DO - 10.1016/j.disc.2013.03.014

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VL - 313

SP - 1429

EP - 1435

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 13

ER -

The excedance algebra

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

Access to Document

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