Large schröder paths by types and symmetric functions

Su Hyung An, Sen Peng Eu, Sangwook Kim

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

In this paper we provide three results involving large Schröder paths. First, we enumerate the number of large Schröder paths by type. Second, we prove that these numbers are the coefficients of a certain symmetric function defined on the staircase skew shape when expanded in elementary symmetric functions. Finally we define a symmetric function on a Fuss path associated with its low valleys and prove that when expanded in elementary symmetric functions the indices are running over the types of all Schröder paths. These results extend their counterparts of Kreweras and Armstrong-Eu on Dyck paths respectively.

Original languageEnglish
Pages (from-to)1229-1240
Number of pages12
JournalBulletin of the Korean Mathematical Society
Volume51
Issue number4
DOIs
Publication statusPublished - 2014

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Keywords

  • Elementary symmetric functions
  • Partial horizontal strips
  • Schröder paths
  • Sparse noncrossing partitions

ASJC Scopus subject areas

  • Mathematics(all)

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