Chung-Feller Property of Schröder Objects

Youngja Park, Sangwook Kim


Large Schröder paths, sparse noncrossing partitions, partial horizontal strips, and $132$-avoiding alternating sign matrices are objects enumerated by Schröder numbers. In this paper we give formula for the number of Schröder objects with given type and number of connected components. The proofs are bijective using Chung-Feller style. A bijective proof for the number of Schröder objects with given type is provided. We also give a combinatorial interpretation for the number of small Schröder paths.


Large and small Schröder paths; Partial horizontal strips; Sparse non-crossing partitions; 132-avoiding alternating sign matrices

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