In this paper, we introduce mixed coloured permutations, permutations with certain coloured cycles, and study the enumerative properties of these combinatorial objects. We derive the generating function, closed forms, recursions and combinatorial identities for the counting sequence, for mixed Stirling numbers of the first kind. In this comprehensive study, we consider further the conditions on the length of the cycles, $r$-mixed Stirling numbers and the connection to Bell polynomials.
Volume 130, 2020
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