Browsing Combinatorics and Optimization by Subject "permutation"
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Genus one partitions
(University of Waterloo, 2006)We obtain a tight upper bound for the genus of a partition, and calculate the number of partitions of maximal genus. The generating series for genus zero and genus one rooted hypermonopoles is obtained in closed form ... -
Transitive Factorizations of Permutations and Eulerian Maps in the Plane
(University of Waterloo, 2005)The problem of counting ramified covers of a Riemann surface up to homeomorphism was proposed by Hurwitz in the late 1800's. This problem translates combinatorially into factoring a permutation with a specified cycle ...