×

zbMATH — the first resource for mathematics

Counting unlabelled chord diagrams of maximal genus. (English. Russian original) Zbl 1410.05006
J. Math. Sci., New York 236, No. 5, 521-526 (2019); translation from Zap. Nauchn. Semin. POMI 464, 77-87 (2017).
Summary: We enumerate maximal chord diagrams up to all isomorphisms. The enumeration formula is based on a bijection between the rooted one-vertex one-face maps on locally orientable surfaces and a certain class of symmetric chord diagrams. This result extends the result of R. Cori and M. Marcus [Theor. Comput. Sci. 204, No. 1–2, 55–73 (1998; Zbl 0913.68148)] on the enumeration of maximal chord diagrams up to rotations.
MSC:
05A15 Exact enumeration problems, generating functions
05C30 Enumeration in graph theory
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Walsh, TRS; Lehman, AB, Counting rooted maps by genus, J. Combin. Theory Ser. B, 13, 192-218, (1972) · Zbl 0228.05108
[2] Harer, J.; Zagier, D., The Euler characteristic of the moduli space of curves, Invent. Math., 85, 457-485, (1986) · Zbl 0616.14017
[3] Cori, R.; Marcus, M., Counting non-isomorphic chord diagrams, Theoret. Comput. Sci., 204, 55-73, (1998) · Zbl 0913.68148
[4] Read, RC, On general dissections of a polygon, Aequationes Math., 18, 370-388, (1978) · Zbl 0396.05028
[5] Wormald, NC, Counting unrooted planar maps, Discrete Math., 36, 205-225, (1981) · Zbl 0467.05034
[6] Liskovets, VA, A reductive technique for enumerating non-isomorphic planar maps, Discrete Math., 156, 197-217, (1996) · Zbl 0857.05044
[7] Ledoux, M., A recursion formula for the moments of the Gaussian orthogonal ensemble, Ann. Inst. H. Poincaré Probab. Statist., 45, 754-769, (2009) · Zbl 1184.60003
[8] Mednykh, A.; Nedela, R., Enumeration of unrooted maps of a given genus, J. Combin. Theory Ser. B, 96, 709-729, (2006) · Zbl 1102.05033
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.