Bijections for Maps with Boundaries: Krikun’s Formula for Triangulations, and a Quadrangulation Analogue

Abstract

We present bijections for planar maps with boundaries. In particular, we obtain bijections for triangulations and quadrangulations of the sphere with boundaries of prescribed lengths. For triangulations we recover the beautiful factorized formula obtained by Krikun using a (technically involved) generating function approach. The analogous formula for… (More)

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