Geodesic
Genus one partitions
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014) (2014).

Voir la notice de l'article provenant de la source Episciences

We prove the conjecture by M. Yip stating that counting genus one partitions by the number of their elements and parts yields, up to a shift of indices, the same array of numbers as counting genus one rooted hypermonopoles. Our proof involves representing each genus one permutation by a four-colored noncrossing partition. This representation may be selected in a unique way for permutations containing no trivial cycles. The conclusion follows from a general generating function formula that holds for any class of permutations that is closed under the removal and reinsertion of trivial cycles. Our method also provides another way to count rooted hypermonopoles of genus one, and puts the spotlight on a class of genus one permutations that is invariant under an obvious extension of the Kreweras duality map to genus one permutations. 
@article{DMTCS_2014_special_265_a29,
     author = {Cori, Robert and Hetyei, G\'abor},
     title = {Genus one partitions},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)},
     year = {2014},
     doi = {10.46298/dmtcs.2404},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2404/}
}
TY  - JOUR
AU  - Cori, Robert
AU  - Hetyei, Gábor
TI  - Genus one partitions
JO  - Discrete mathematics & theoretical computer science
PY  - 2014
VL  - DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2404/
DO  - 10.46298/dmtcs.2404
LA  - en
ID  - DMTCS_2014_special_265_a29
ER  - 
%0 Journal Article
%A Cori, Robert
%A Hetyei, Gábor
%T Genus one partitions
%J Discrete mathematics & theoretical computer science
%D 2014
%V DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2404/
%R 10.46298/dmtcs.2404
%G en
%F DMTCS_2014_special_265_a29
Cori, Robert; Hetyei, Gábor. Genus one partitions. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014) (2014). doi : 10.46298/dmtcs.2404. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2404/

Cité par Sources :