Exact forbidden subposet results using Chain decompositions of the Cycle
Combinatorics
2014-11-04 v1
Abstract
We introduce a method of decomposing the family of intervals along a cyclic permutation into chains to determine the size of the largest family of subsets of not containing one or more given posets as a subposet. De Bonis, Katona and Swanepoel determined the size of the largest butterfly-free family. We strengthen this result by showing that, for certain posets containing the butterfly poset as a subposet, the same bound holds. We also obtain the corresponding LYM-type inequalities.
Keywords
Cite
@article{arxiv.1411.0415,
title = {Exact forbidden subposet results using Chain decompositions of the Cycle},
author = {Abhishek Methuku and Casey Tompkins},
journal= {arXiv preprint arXiv:1411.0415},
year = {2014}
}