We present a method of computing the generating function $f_P(\textbf{x})$ of $P$-partitions of a poset $P$. The idea is to introduce two kinds of transformations on posets and compute $f_P(\textbf{x})$ by recursively applying these transformations. As an application, we consider the partially ordinal sum $P_n$ of $n$ copies of a given poset, which generalizes both the direct sum and the ordinal sum. We show that the sequence $\{f_{P_n}(\textbf{x})\}_{n\ge 1}$ satisfies a finite system of recurrence relations with respect to $n$. We illustrate the method by several examples, including a kind of $3$-rowed posets and the multi-cube posets.
@article{10_37236_2524,
author = {Daniel K. Du and Qing-Hu Hou},
title = {Partially ordinal sums and {\(P\)-partitions}},
journal = {The electronic journal of combinatorics},
year = {2012},
volume = {19},
number = {4},
doi = {10.37236/2524},
zbl = {1267.05023},
url = {http://geodesic.mathdoc.fr/articles/10.37236/2524/}
}
TY - JOUR
AU - Daniel K. Du
AU - Qing-Hu Hou
TI - Partially ordinal sums and \(P\)-partitions
JO - The electronic journal of combinatorics
PY - 2012
VL - 19
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/2524/
DO - 10.37236/2524
ID - 10_37236_2524
ER -
%0 Journal Article
%A Daniel K. Du
%A Qing-Hu Hou
%T Partially ordinal sums and \(P\)-partitions
%J The electronic journal of combinatorics
%D 2012
%V 19
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/2524/
%R 10.37236/2524
%F 10_37236_2524
Daniel K. Du; Qing-Hu Hou. Partially ordinal sums and \(P\)-partitions. The electronic journal of combinatorics, Tome 19 (2012) no. 4. doi: 10.37236/2524
