Mathematics – Combinatorics
Scientific paper
2001-06-06
J. Combinatorial Theory ser. A, 98 (2002), 106--117
Mathematics
Combinatorics
10 pages, 3 figures
Scientific paper
We provide a bijection between the set of factorizations, that is, ordered (n-1)-tuples of transpositions in ${\mathcal S}_{n}$ whose product is (12...n), and labelled trees on $n$ vertices. We prove a refinement of a theorem of D\'{e}nes 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 bijection to leaf edges of a tree. Moreover, we give a generalization of this fact.
Goulden Ian
Yong Alexander
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