Pure-cycle Hurwitz factorizations and multi-noded rooted trees

Details Pure-cycle Hurwitz factorizations and multi-noded rooted trees Pure-cycle Hurwitz factorizations and multi-noded rooted trees

2010-08-22

arxiv.org/abs/1008.3677v2

Mathematics

Combinatorics

20 pages, 5 figures

Scientific paper

Pure-cycle Hurwitz number counts the number of connected branched covers of the projective lines where each branch point has only one ramification point over it. The main result of the paper is that when the genus is $0$ and one of the ramification indices is $d,$ the degree of the covers, the pure-cycle Hurwitz number is $d^{r-3},$ where $r$ is the number of branch points. We approach this problem via the standard translation of Hurwitz numbers into group theory. We define a new class of combinatorial objects, multi-noded rooted trees, which generalize rooted trees. We find the cardinality of this new class which with proper parameters is exactly $d^{r-2}.$ The main part of this paper is the proof that there is a bijection from factorizations of a $d$-cycle to multi-noded rooted trees via factorization graphs. This implies the desired formula.

Affiliated with

Also associated with

No associations

Rating

Pure-cycle Hurwitz factorizations and multi-noded rooted trees does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Pure-cycle Hurwitz factorizations and multi-noded rooted trees, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Pure-cycle Hurwitz factorizations and multi-noded rooted trees will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-165719