An independent set C of vertices in a graph is an efficient dominating set (or perfect code) when each vertex not in C is adjacent to exactly one vertex in C. An E-chain is a countable family ofâ€¦ (More)

We prove a removal lemma for systems of linear equations over finite fields: let X1, . . . , Xm be subsets of the finite field Fq and let A be a (kÃ—m) matrix with coefficients in Fq and rank k; ifâ€¦ (More)

Let A = {a1, . . . , ak} and B = {b1, . . . , bk} be two subsets of an Abelian group G, k â‰¤ |G|. Snevily conjectured that, when G is of odd order, there is a permutation Ï€ âˆˆ Sk such that the sums aiâ€¦ (More)

Let S, T be subsets of Z/pZ with min{|S|, |T |} > 1. The Cauchyâ€“Davenport theorem states that |S + T | â‰¥ min{p, |S| + |T | âˆ’ 1}. A theorem by Vosper characterizes the critical pair in the aboveâ€¦ (More)

We show that the number of monochromatic solutions of the equation x1 1 x Î±2 2 Â· Â· Â·xÎ±r r = g in a 2-coloring of a finite group G, where Î±1, . . . , Î±r are permutations and g âˆˆ G, depends only on theâ€¦ (More)

Optical absorption and fluorescence spectroscopies were employed in the study of the interaction between synthetic L-dopa (dihydroxyphenylalanine) melanin and the cationic porphyrinsâ€¦ (More)

We are interested in characterising pairs S, T of F -linear subspaces in a field extension L/F such that the linear span ST of the set of products of elements of S and of elements of T has smallâ€¦ (More)