Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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LARGE SCHRÖDER PATHS BY TYPES AND SYMMETRIC FUNCTIONS

  • An, Su Hyung (Department of Mathematics Yonsei University) ;
  • Eu, Sen-Peng (Department of Mathematics National Taiwan Normal University) ;
  • Kim, Sangwook (Department of Mathematics Chonnam National University)
  • Received : 2013.11.19
  • Published : 2014.07.31
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Abstract

In this paper we provide three results involving large Schr$\ddot{o}$der paths. First, we enumerate the number of large Schr$\ddot{o}$der 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 Schr$\ddot{o}$der paths. These results extend their counterparts of Kreweras and Armstrong-Eu on Dyck paths respectively.

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References

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