Mathematics – Combinatorics
Scientific paper
2011-01-19
Mathematics
Combinatorics
23 pages, 9 figures
Scientific paper
We evaluate combinatorially certain connection coefficients of the symmetric group that count the number of factorizations of a long cycle as a product of three permutations. Such factorizations admit an important topological interpretation in terms of unicellular constellations on orientable surfaces. Bijective computations of these coefficients are so far limited to very special cases. Thanks to a new bijection that refines the work of Schaeffer and Vassilieva in \cite{SV} and \cite{SV2}, we give an explicit closed form evaluation of the generating series for these coefficients. The main ingredient in the bijection is a modified oriented tricolored tree tractable to enumerate. Finally, reducing this bijection to factorizations of a long cycle into two permutations, we get the analogue formula for the corresponding generating series.
Morales Alejandro H.
Vassilieva Ekaterina A.
No associations
LandOfFree
Direct bijective computation of the generating series for 2 and 3-connection coefficients of the symmetric group 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 Direct bijective computation of the generating series for 2 and 3-connection coefficients of the symmetric group, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Direct bijective computation of the generating series for 2 and 3-connection coefficients of the symmetric group will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-156004