Generating functions of hypermaps and m-constellations with two alternating boundaries
Chebasov Dmitry
Source abstract
We study the enumeration of planar hypermaps with several alternating boundaries. We first derive a peeling recursion with an arbitrary number of alternating boundaries and, in the two- boundary case, translate it into a functional equation for the corresponding generating function. Our main result is an explicit solution of this equation for m-constellations. In particular, we obtain a rational expression for the genus-zero two-point function, or cylinder generating function, with two alternating boundaries.
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