Inclusion-exclusion by ordering-free cancellation
Combinatorics
2018-01-16 v1
Abstract
Whitney's broken circuit theorem gives a graphical example to reduce the number of the terms in the sum of the inclusion-exclusion formula by a predicted cancellation. So far, the known cancellations for the formula strongly depend on the prescribed (linear or partial) ordering on the index set. We give a new cancellation method, which does not require any ordering on the index set. Our method extends all the `ordering-based' methods known in the literatures and in general reduces more terms. As examples, we use our method to improve some relevant results on graph polynomials.
Cite
@article{arxiv.1801.04706,
title = {Inclusion-exclusion by ordering-free cancellation},
author = {Yin Chen and Jianguo Qian},
journal= {arXiv preprint arXiv:1801.04706},
year = {2018}
}