On quasi-polynomials counting planar tight maps Article Swipe
Jérémie Bouttier
,
Emmanuel Guitter
,
Grégory Miermont
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.5070/c64163849
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.5070/c64163849
A tight map is a map with some of its vertices marked, such that every vertex of degree \\(1\\) is marked. We give an explicit formula for the number \\(N_{0,n}(d_1,\\ldots,d_n)\\) of planar tight maps with \\(n\\) labeled faces of prescribed degrees \\(d_1,\\ldots,d_n\\), where a marked vertex is seen as a face of degree \\(0\\). It is a quasi-polynomial in \\((d_1,\\ldots,d_n)\\), as shown previously by Norbury. Our derivation is bijective and based on the slice decomposition of planar maps. In the non-bipartite case, we also rely on enumeration results for two-type forests. We discuss the connection with the enumeration of non necessarily tight maps. In particular, we provide a generalization of Tutte's classical slicings formula to all non-bipartite maps.Mathematics Subject Classifications: 05A15, 05A19Keywords: Planar maps, bijective enumeration, slice decomposition
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- en
- Landing Page
- https://doi.org/10.5070/c64163849
- https://escholarship.org/content/qt9h946160/qt9h946160.pdf?t=sfxprn
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On quasi-polynomials counting planar tight mapsWork title
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articleOpenAlex work type
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enPrimary language
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2024Year of publication
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2024-07-01Full publication date if available
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Jérémie Bouttier, Emmanuel Guitter, Grégory MiermontList of authors in order
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https://escholarship.org/content/qt9h946160/qt9h946160.pdf?t=sfxprnDirect link to full text PDF
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Planar, Mathematics, Combinatorics, Computer science, Computer graphics (images)Top concepts (fields/topics) attached by OpenAlex
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| primary_location.raw_source_name | Combinatorial Theory |
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| publication_date | 2024-07-01 |
| publication_year | 2024 |
| referenced_works | https://openalex.org/W3041597759, https://openalex.org/W3104703509, https://openalex.org/W1993114066, https://openalex.org/W3152803879, https://openalex.org/W2142949475, https://openalex.org/W3117798398, https://openalex.org/W3037392287, https://openalex.org/W2057266558, https://openalex.org/W1962027554, https://openalex.org/W2167929644, https://openalex.org/W1997713922, https://openalex.org/W2006442667, https://openalex.org/W186403072, https://openalex.org/W1585244820, https://openalex.org/W3098932440, https://openalex.org/W3204062795, https://openalex.org/W2118998907, https://openalex.org/W1551177513, https://openalex.org/W2042456974, https://openalex.org/W2994857158, https://openalex.org/W2078463495, https://openalex.org/W3103616215, https://openalex.org/W2086284603, https://openalex.org/W2152585937, https://openalex.org/W3106242067, https://openalex.org/W1972563066 |
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