Geodesic
Counting unlabelled chord diagrams of maximal genus
Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part IX, Tome 464 (2017), pp. 77-87

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Maximal chord diagrams up to all isomorphisms are enumerated. The enumerating formula is based on a bijection between rooted one-vertex one-face maps on locally orientable surfaces and a certain class of symmetric chord diagrams. This result extends the one of Cori and Marcus regarding maximal chord diagrams enumerated up to rotations. 
@article{ZNSL_2017_464_a3,
     author = {E. C. Krasko},
     title = {Counting unlabelled chord diagrams of maximal genus},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {77--87},
     publisher = {mathdoc},
     volume = {464},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_464_a3/}
}
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E. C. Krasko. Counting unlabelled chord diagrams of maximal genus. Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part IX, Tome 464 (2017), pp. 77-87. http://geodesic.mathdoc.fr/item/ZNSL_2017_464_a3/