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.
@article{10_37236_5659,
author = {Youngja Park and Sangwook Kim},
title = {Chung-Feller property of {Schr\"oder} objects},
journal = {The electronic journal of combinatorics},
year = {2016},
volume = {23},
number = {2},
doi = {10.37236/5659},
zbl = {1338.05011},
url = {http://geodesic.mathdoc.fr/articles/10.37236/5659/}
}
TY - JOUR
AU - Youngja Park
AU - Sangwook Kim
TI - Chung-Feller property of Schröder objects
JO - The electronic journal of combinatorics
PY - 2016
VL - 23
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/5659/
DO - 10.37236/5659
ID - 10_37236_5659
ER -
%0 Journal Article
%A Youngja Park
%A Sangwook Kim
%T Chung-Feller property of Schröder objects
%J The electronic journal of combinatorics
%D 2016
%V 23
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/5659/
%R 10.37236/5659
%F 10_37236_5659
Youngja Park; Sangwook Kim. Chung-Feller property of Schröder objects. The electronic journal of combinatorics, Tome 23 (2016) no. 2. doi: 10.37236/5659
