English

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 [n]:={1,2,...,n}[n]:= \{1,2,...,n\} 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}
}