منابع مشابه
Tree-like Properties of Cycle Factorizations
We provide a bijection between the set of factorizations, that is, ordered (n− 1)-tuples of transpositions in Sn whose product is (12...n), and labelled trees on n vertices. We prove a refinement of a theorem of Dénes [3] that establishes new tree-like properties of factorizations. In particular, we show that a certain class of transpositions of a factorization correspond naturally under our bi...
متن کاملOn inequivalent factorizations of a cycle
We introduce a bijection between inequivalent minimal factorizations of the n-cycle (1 2 . . . n) into a product of smaller cycles of given length and trees of a certain structure. A factorization has the type α = (α2, α3, · · · ) if it has αj factors of length j. Inequivalent factorizations are defined up to reordering of commuting factors. A factorization is minimal if no factorizations of a ...
متن کاملCycle factorizations and one-faced graph embeddings
Consider factorizations into transpositions of an n-cycle in the symmetric group Sn. To every such factorization we assign a monomial in variables wij that retains the transpositions used, but forgets their order. Summing over all possible factorizations of n-cycles we obtain a polynomial that happens to admit a closed expression. From this expression we deduce a formula for the number of 1-fac...
متن کاملTransitive cycle factorizations and prime parking functions
Minimal transitive cycle factorizations and parking functions are related very closely. Using the correspondence between them, we find a bijection between minimal transitive factorizations of permutations of type (1, n − 1) and prime parking functions of length n.
متن کاملCycle factorizations and 1-faced graph embeddings
Consider factorizations into transpositions of an n-cycle in the symmetric group Sn. To every such factorization we assign a monomial in variables wij that retains the transpositions used, but forgets their order. Summing over all possible factorizations of n-cycles we obtain a polynomial that happens to admit a closed expression. From this expression we deduce a formula for the number of 1-fac...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1998
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(98)00053-3