Refined Enumeration of Minimal Transitive Factorizations of Permutations
نویسنده
چکیده
Minimal transitive cycle factorizations, parking functions and labeled trees are related very closely. Using the correspondences between them, we find a refined enumeration of minimal transitive factorizations of permutations of type (1, n− 1) and (2, n− 2).
منابع مشابه
Combinatorial Constructions for Transitive Factorizations in the Symmetric Group
We consider the problem of counting transitive factorizations of permutations; that is, we study tuples (σr , . . . , σ1) of permutations on {1, . . . , n} such that (1) the product σr · · · σ1 is equal to a given target permutation π , and (2) the group generated by the factors σi acts transitively on {1, . . . , n}. This problem is widely known as the Hurwitz Enumeration Problem, since an enc...
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