Exact Face-isoperimetric Inequalities


A d-dimensional face of the grid [k]n = {0, ... , k−s1}n is a set of the form {X ∈ [k]n}:xi1=a1..., xid =ad, where 1 ⩽ i1 < … < id ⩽ n and a1, … , ad ∈ [k]. The main aim of this note is to give a best possible upper bound for the number of d-dimensional faces contained in a subset of [k]n of given cardinality, and thereby to prove a conjecture of Bollobás and Radcliffe. © 1990, Academic Press Limited. All rights reserved.

Publication Title

European Journal of Combinatorics