# Separation probabilities and analogues of a Zagier-Stanley formula

29 Sep 2019 Chen Ricky X. F.

In this paper, we first obtain some analogues of a formula of Zagier (1995) and Stanley (2011). For instance, we prove that the number of pairs of $n$-cycles whose product has $k$ cycles and has $m$ given elements contained in distinct cycles (or separated) is given by  \frac{2 (n-1)!.. (read more)

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