Exact Face-isoperimetric Inequalities
Abstract
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
Recommended Citation
Bollobás, B., & Leader, I. (1990). Exact Face-isoperimetric Inequalities. European Journal of Combinatorics, 11 (4), 335-340. https://doi.org/10.1016/S0195-6698(13)80135-7
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