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- Shalom Eliahou, Michel Kervaire, Bahman Saffari
- J. Comb. Theory, Ser. A
- 1990

- Shalom Eliahou
- Discrete Mathematics
- 1993

Eliahou, S., The 3x+ 1 problem: new lower bounds on nontrivial cycle lengths, Discrete Mathematics 118 (1993) 45556. Let 7’: N -+ N be the function defined by T(n) = n/2 if n is even, T(n) = (3n + 1)/2 if n is odd. We show, among other things, that any nontrivial cyclic orbit under iteration of T must contain at least 17 087 915 elements.

- Shalom Eliahou
- Eur. J. Comb.
- 1999

For each k ≥ 2, we exhibit infinite families of prime k-component links with Jones polynomial equal to that of the k-component unlink.

- Shalom Eliahou
- 2006

A matching in a group G is a bijection φ from a subset A to a subset B in G such that aφ(a) / ∈ A for all a ∈ A. The group G is said to have the matching property if, for any finite subsets A,B in G of same cardinality with 1 / ∈ B, there is a matching from A to B. Using tools from additive number theory, Losonczy proved a few years ago that the only… (More)

- Shalom Eliahou, Delphine Hachez
- Experimental Mathematics
- 2004

- Roland Bacherand, Shalom Eliahou
- 2009

In this paper we solve, by computational means, an open problem of Erickson: denoting [n] = {1, . . . , n}, what is the smallest integer n0 such that, for every n ≥ n0 and every 2-coloring of the grid [n]× [n], there is a constant 2-square, i.e. a 2 × 2 subgrid S = {i, i + t} × {j, j + t} whose four points are colored the same? It has been shown recently… (More)

- Shalom Eliahou, Michel Kervaire
- Electronic Notes in Discrete Mathematics
- 2007

The Cauchy-Davenport theorem states that, if p is prime and A,B are nonempty subsets of cardinality r, s in Z/pZ, the cardinality of the sumset A + B = {a + b | a ∈ A, b ∈ B} is bounded below by min(r+ s− 1, p); moreover, this lower bound is sharp. Natural extensions of this result consist in determining, for each group G and positive integers r, s ≤ |G|,… (More)

- Shalom Eliahou, Michel Kervaire
- Eur. J. Comb.
- 2006

Let Dn be the dihedral group of order 2n. For all integers r, s such that 1 ≤ r, s ≤ 2n, we give an explicit upper bound for the minimal size μDn (r, s) = min |A · B| of sumsets (product sets) A · B, where A and B range over all subsets of Dn of cardinality r and s respectively. It is shown by construction that μDn (r, s) is bounded above by the known value… (More)

- Shalom Eliahou
- 2008

Let K ⊂ L be a field extension. Given K-subspaces A,B of L, we study the subspace 〈AB〉 spanned by the product set AB = {ab | a ∈ A, b ∈ B}. We obtain some lower bounds on dimK〈AB〉 and dimK〈B 〉 in terms of dimK A, dimK B and n. This is achieved by establishing linear versions of constructions and results in additive number theory mainly due to Kemperman and… (More)