We give bounds on the number of distinct differences Na − a as a varies over all elements of a given finite set A ⊆ (R/Z)d, d ≥ 1, and Na is a nearest neighbour to a.

Combinatorics, Probability and Computing / Volume 7 / Issue 03 / September 1998, pp 247 260 DOI: null, Published online: 08 September 2000 Link to this article: http://journals.cambridge.org/abstract_S0963548398003575 How to cite this article: P. FRANKL and N. TOKUSHIGE (1998). Some Inequalities Concerning Cross-Intersecting Families. Combinatorics, Probability and Computing, 7, pp 247-260 Requ...

We prove bounds for multilinear operators on R given by multipliers which are singular along a k dimensional subspace. The new case of interest is when the rank k/d is not an integer. Connections with the concept of true complexity from Additive Combinatorics are also investigated.

We give a brief overview of the life and combinatorics Jeff Remmel, mathematician with successful careers in both logic combinatorics.

Let Zn denote the ring of integers modulo n. A permutation of Zn is a sequence of n distinct elements of Zn. Addition and subtraction of two permutations is defined element-wise. In this paper we consider two extremal problems on permutations of Zn, namely, the maximum size of a collection of permutations such that the sum of any two distinct permutations in the collection is again a permutatio...