Bijective enumeration of constellations in higher genus

Authors

  • Jordi Castellví Universitat Politécnica de Catalunya (UPC)

Keywords:

combinatorics, maps, enumeration, bijection, blossoming map, constellation, rationality.

Abstract

Bousquet-Mélou and Schaeffer gave in 2000 a bijective enumeration of some planar maps called constellations. In 2019, Lepoutre described a bijection between bicolorable maps of arbitrary genus and some unicellular maps of the same genus. We present a bijection between constellations of higher genus and some unicellular maps that generalizes both existing bijections at the same time. Using this bijection, we manage to enumerate a subclass of constellations on the torus, proving that its generating function is a rational function of the generating function of some trees.

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How to Cite

Castellví, J. (2022). Bijective enumeration of constellations in higher genus. Reports@SCM, 7(1), 13–25. Retrieved from https://revistes.iec.cat/index.php/reports/article/view/150090

Issue

Vol. 7 No. 1 (2022)

Section

Articles

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