In this paper denotes a surface homeomorphic to a punctured torus or a pair of pants. Our interest is the study of combinatorial -systoles, that is closed curves with self-intersection numbers greater than and with least combinatorial length. We show that the maximal intersection number of combinatorial -systoles of grows like and .
This result, in case of a pair of pants and a punctured torus, is a positive response to the combinatorial version of the Erlandsson-Parlier conjecture, originally formulated for the geometric length.
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@article{CML_2021__13_2_29_0,
author = {ElHadji Abdou Aziz Diop and Masseye Gaye and Abdoul Karim Sane},
title = {Combinatorial $k$-systoles on a punctured torus and a pair of pants},
journal = {Confluentes Mathematici},
pages = {29--38},
publisher = {Institut Camille Jordan},
volume = {13},
number = {2},
year = {2021},
doi = {10.5802/cml.76},
language = {en},
url = {https://cml.centre-mersenne.org/articles/10.5802/cml.76/}
}
TY - JOUR AU - ElHadji Abdou Aziz Diop AU - Masseye Gaye AU - Abdoul Karim Sane TI - Combinatorial $k$-systoles on a punctured torus and a pair of pants JO - Confluentes Mathematici PY - 2021 SP - 29 EP - 38 VL - 13 IS - 2 PB - Institut Camille Jordan UR - https://cml.centre-mersenne.org/articles/10.5802/cml.76/ DO - 10.5802/cml.76 LA - en ID - CML_2021__13_2_29_0 ER -
%0 Journal Article %A ElHadji Abdou Aziz Diop %A Masseye Gaye %A Abdoul Karim Sane %T Combinatorial $k$-systoles on a punctured torus and a pair of pants %J Confluentes Mathematici %D 2021 %P 29-38 %V 13 %N 2 %I Institut Camille Jordan %U https://cml.centre-mersenne.org/articles/10.5802/cml.76/ %R 10.5802/cml.76 %G en %F CML_2021__13_2_29_0
ElHadji Abdou Aziz Diop; Masseye Gaye; Abdoul Karim Sane. Combinatorial $k$-systoles on a punctured torus and a pair of pants. Confluentes Mathematici, Tome 13 (2021) no. 2, pp. 29-38. doi : 10.5802/cml.76. https://cml.centre-mersenne.org/articles/10.5802/cml.76/
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