In this paper we enumerate the number of $(k, r)$-Fuss-Schröder paths of type $\lambda$. Y. Park and S. Kim studied small Schröder paths with type $\lambda$. Generalizing the results to small $(k, r)$-Fuss-Schröder paths with type $\lambda$, we give a combinatorial interpretation for the number of small $(k, r)$-Fuss-Schröder paths of type $\lambda$ by using Chung-Feller style. We also give two sets of sparse noncrossing partitions of $[2(k + 1)n + 1]$ and $[2(k + 1)n + 2]$ which are in bijection with the set of all small and large, respectively, $(k, r)$-Fuss-Schröder paths of type $\lambda$.
@article{10_37236_6719,
author = {Suhyung An and JiYoon Jung and Sangwook Kim},
title = {Enumeration of {Fuss-Schr\"oder} paths},
journal = {The electronic journal of combinatorics},
year = {2017},
volume = {24},
number = {2},
doi = {10.37236/6719},
zbl = {1364.05004},
url = {http://geodesic.mathdoc.fr/articles/10.37236/6719/}
}
TY - JOUR
AU - Suhyung An
AU - JiYoon Jung
AU - Sangwook Kim
TI - Enumeration of Fuss-Schröder paths
JO - The electronic journal of combinatorics
PY - 2017
VL - 24
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/6719/
DO - 10.37236/6719
ID - 10_37236_6719
ER -
%0 Journal Article
%A Suhyung An
%A JiYoon Jung
%A Sangwook Kim
%T Enumeration of Fuss-Schröder paths
%J The electronic journal of combinatorics
%D 2017
%V 24
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/6719/
%R 10.37236/6719
%F 10_37236_6719
Suhyung An; JiYoon Jung; Sangwook Kim. Enumeration of Fuss-Schröder paths. The electronic journal of combinatorics, Tome 24 (2017) no. 2. doi: 10.37236/6719
