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1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

Abstract : We give a bijective proof of the fact that the number of k-prefixes of minimal factorisations of the n-cycle 1

.n as a product of n-1 transpositions is n^{k-1}\binom{n}{k+1}. Rather than a bijection, we construct a surjection with fibres of constant size. This surjection is inspired by a bijection exhibited by Stanley between minimal factorisations of an n-cycle and parking functions, and by a counting argument for parking functions due to Pollak.

Author: Thierry Lévy -



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