The excedance algebra

Eric Clark, Richard Ehrenborg

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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.

Original languageEnglish
Pages (from-to)1429-1435
Number of pages7
JournalDiscrete Mathematics
Issue number13
StatePublished - 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 .


  • 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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