TY - JOUR
T1 - Tree-like properties of cycle factorizations
AU - Goulden, Ian
AU - Yong, Alexander
N1 - Funding Information:
This work was supported by the Natural Sciences and Engineering Research Council of Canada, through a grant to I.G., and a PGSA to A.Y. This work was partially completed while A.Y. was visiting the Fields Institute in Toronto. We thank Gilles Schaeffer for helpful discussions. References [2, 5] were brought to our attention by an anonymous referee, who made other helpful suggestions.
PY - 2002
Y1 - 2002
N2 - We provide a bijection between the set of factorizations, that is, ordered (n - 1)-tuples of transpositions in ?n whose product is (12...n), and labelled trees on n vertices. We prove a refinement of a theorem of J. Dénes (1959, Publ. Math. Inst. Hungar. Acad. Sci. 4, 63-71) that establishes new tree-like properties of factorizations. In particular, we show that a certain class of transpositions of a factorization corresponds naturally under our bijection to leaf edges (incident with a vertex of degree 1) of a tree. Moreover, we give a generalization of this fact.
AB - We provide a bijection between the set of factorizations, that is, ordered (n - 1)-tuples of transpositions in ?n whose product is (12...n), and labelled trees on n vertices. We prove a refinement of a theorem of J. Dénes (1959, Publ. Math. Inst. Hungar. Acad. Sci. 4, 63-71) that establishes new tree-like properties of factorizations. In particular, we show that a certain class of transpositions of a factorization corresponds naturally under our bijection to leaf edges (incident with a vertex of degree 1) of a tree. Moreover, we give a generalization of this fact.
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U2 - 10.1006/jcta.2001.3230
DO - 10.1006/jcta.2001.3230
M3 - Article
AN - SCOPUS:0036256830
SN - 0097-3165
VL - 98
SP - 106
EP - 117
JO - Journal of Combinatorial Theory. Series A
JF - Journal of Combinatorial Theory. Series A
IS - 1
ER -