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 $[n]$ 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.
@article{10_37236_4803,
author = {Abhishek Methuku and Casey Tompkins},
title = {Exact forbidden subposet results using chain decompositions of the cycle},
journal = {The electronic journal of combinatorics},
year = {2015},
volume = {22},
number = {4},
doi = {10.37236/4803},
zbl = {1329.05293},
url = {http://geodesic.mathdoc.fr/articles/10.37236/4803/}
}
TY - JOUR
AU - Abhishek Methuku
AU - Casey Tompkins
TI - Exact forbidden subposet results using chain decompositions of the cycle
JO - The electronic journal of combinatorics
PY - 2015
VL - 22
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/4803/
DO - 10.37236/4803
ID - 10_37236_4803
ER -
%0 Journal Article
%A Abhishek Methuku
%A Casey Tompkins
%T Exact forbidden subposet results using chain decompositions of the cycle
%J The electronic journal of combinatorics
%D 2015
%V 22
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/4803/
%R 10.37236/4803
%F 10_37236_4803
Abhishek Methuku; Casey Tompkins. Exact forbidden subposet results using chain decompositions of the cycle. The electronic journal of combinatorics, Tome 22 (2015) no. 4. doi: 10.37236/4803
