Pattern Matching in the Cycle Structures of Permutations
نویسندگان
چکیده
In this paper, we study pattern matching conditions in the cycle structures of permutations. We develop methods to find the joint distribution of the number of cycles and the number of cycle descents over the set of permutations in the symmetric group Sn which have no cycle occurrences or no consecutive cycle occurrences of a given pattern or set of patterns. Our methods also allow us to refine some results on the enumeration of permutations of Sn which have no occurrences or no consecutive occurrences of classical patterns in permutations in the case where the pattern starts with 1.
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