LARGE SCHR¨ODER PATHS BY TYPES AND SYMMETRIC FUNCTIONS

다국어 초록 (Multilingual Abstract)

In this paper we provide three results involving large Schr¨oder paths. First, we enumerate the number of large Schr¨oder 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¨oder paths. These results extend their counterparts of Kreweras and Armstrong-Eu on Dyck paths respectively.

참고문헌 (Reference)

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