Linear inequalities for flags in graded posets
Abstract
The closure of the convex cone generated by all flag $f$vectors of graded posets is shown to be polyhedral. In particular, we give the facet inequalities to the polar cone of all nonnegative chainenumeration functionals on this class of posets. These are in onetoone correspondence with antichains of intervals on the set of ranks and thus are counted by Catalan numbers. Furthermore, we prove that the convolution operation introduced by Kalai assigns extreme rays to pairs of extreme rays in most cases. We describe the strongest possible inequalities for graded posets of rank at most 5.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 1997
 DOI:
 10.48550/arXiv.math/9706220
 arXiv:
 arXiv:math/9706220
 Bibcode:
 1997math......6220B
 Keywords:

 Mathematics  Combinatorics