The Legendre-Stirling numbers of the second kind were introduced by Everitt et al. in the spectral theory of powers of the Legendre differential expressions. As a continuation of the work of Andrews and Littlejohn (Proc. Amer. Math. Soc., 137 (2009), 2581-2590), we provide a combinatorial code for Legendre-Stirling set partitions. As an application, we obtain expansions of the Legendre-Stirling numbers of both kinds in terms of binomial coefficients.
@article{10_37236_8060,
author = {Shi-Mei Ma and Jun Ma and Yeong-Nan Yeh},
title = {On certain combinatorial expansions of the {Legendre-Stirling} numbers},
journal = {The electronic journal of combinatorics},
year = {2018},
volume = {25},
number = {4},
doi = {10.37236/8060},
zbl = {1409.05029},
url = {http://geodesic.mathdoc.fr/articles/10.37236/8060/}
}
TY - JOUR
AU - Shi-Mei Ma
AU - Jun Ma
AU - Yeong-Nan Yeh
TI - On certain combinatorial expansions of the Legendre-Stirling numbers
JO - The electronic journal of combinatorics
PY - 2018
VL - 25
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/8060/
DO - 10.37236/8060
ID - 10_37236_8060
ER -
%0 Journal Article
%A Shi-Mei Ma
%A Jun Ma
%A Yeong-Nan Yeh
%T On certain combinatorial expansions of the Legendre-Stirling numbers
%J The electronic journal of combinatorics
%D 2018
%V 25
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/8060/
%R 10.37236/8060
%F 10_37236_8060
Shi-Mei Ma; Jun Ma; Yeong-Nan Yeh. On certain combinatorial expansions of the Legendre-Stirling numbers. The electronic journal of combinatorics, Tome 25 (2018) no. 4. doi: 10.37236/8060
