Abstract
IfA is a family ofk-element subsets of a finite setM having elements of several different types (i.e., amultiset) and ΔA is the set of all (k−1)-element subsets ofM obtainable by removing a single element ofM from a single member ofA, then, according to the well known normalized matching condition, the density ofA among thek-element subsets ofM never exceeds the density of ΔA among the (k−1)-element subsets ofM. We show that this useful fact can be regarded as yet another corollary of the generalized Macaulay theorem.
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