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Generating functions of hypermaps and m-constellations with two alternating boundaries

  • Chebasov Dmitry
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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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Cite

BibTeXRIS
BibTeX
@misc{dmitry2026generating,
  title = {{Generating functions of hypermaps and m-constellations with two alternating boundaries}},
  author = {Chebasov Dmitry},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.22493},
  eprint = {2610.22493},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.22493},
}
RIS
TY  - UNPB
TI  - Generating functions of hypermaps and m-constellations with two alternating boundaries
AU  - Chebasov Dmitry
PY  - 2026
DA  - 2026/10/15
PB  - arXiv
DO  - 10.48550/arxiv.2610.22493
UR  - https://arxiv.org/abs/2610.22493
AB  - 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.
ER  -