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    Plagne, Alain Serra, Oriol and Zémor, Gilles 2013. Yahya Ould Hamidoune’s mathematical journey: A critical review of his work. European Journal of Combinatorics, Vol. 34, Issue. 8, p. 1207.

  • Combinatorics, Probability and Computing, Volume 20, Issue 6
  • November 2011, pp. 855-865

Counting Certain Pairings in Arbitrary Groups

  • Y. O. HAMIDOUNE (a1)
  • DOI:
  • Published online: 11 October 2011

In this paper, we study certain pairings which are defined as follows: if A and B are finite subsets of an arbitrary group, a Wakeford–Fan–Losonczy pairing from B onto A is a bijection φ : BA such that bφ(b) ∉ A, for every bB. The number of such pairings is denoted by μ(B, A).

We investigate the quantity μ(B, A) for A and B, two finite subsets of an arbitrary group satisfying 1 ∉ B, |A| = |B|, and the fact that the order of every element of B is ≥ |B| + 1. Extending earlier results, we show that in this case, μ(B, A) is never equal to 0. Furthermore we prove an explicit lower bound on μ(B, A) in terms of |B| and the cardinality of the group generated by B, which is valid unless A and B have a special form explicitly described. In the case A = B, our bound holds unless B is a translate of a progression.

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[2]S. Eliahou and C. Lecouvey (2008) Matchings in arbitrary groups. Adv. Appl. Math. 40 219224.

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Combinatorics, Probability and Computing
  • ISSN: 0963-5483
  • EISSN: 1469-2163
  • URL: /core/journals/combinatorics-probability-and-computing
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