Uwe Leck
A property of colored complexes and their duals
Preprint series: Preprints aus dem Fachbereich Mathematik, Universität Rostock

MSC:

06A07 Combinatorics of partially ordered sets

Abstract: A ranked poset P is a Macaulay poset if there is a linear oder < of
the elements of P such that for any m, i the set C(m,i) of the m
(with respect to <) smallest elements of rank i has minimum-sized
shadow among all m-element subsets of the i-th level, and the shadow
of C(m,i) consists of the smallest elements of the (i-1)-st level.
P is called shadow-increasing if for all m,i the shadow C(m,i) is not
smaller than the shadow of C(m,i-1). We show that colored complexes
and their duals, the star posets, are shadow-increasing.
Keywords: Macaulay Posets, colored complex. star poset