Prefixes of minimal factorisations of a cycleReport as inadecuate




Prefixes of minimal factorisations of a cycle - Download this document for free, or read online. Document in PDF available to download.

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 -

Source: https://hal.archives-ouvertes.fr/



DOWNLOAD PDF




Related documents