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Sib. Èlektron. Mat. Izv., 2018, Volume 15, Pages 277–304 (Mi semr917)  

Discrete mathematics and mathematical cybernetics

Irreducible triangulations of the once-punctured torus

S. Lawrencenkoa, T. Sulankeb, M. T. Villarc, L. V. Zgonnika, M. J. Chávezc, J. R. Portilloc

a Russian State University of Tourism and Service, Institute for Tourism and Hospitality, Kronstadt Boulevard, 32A, Moscow, 125438, Russia
b Department of Physics, Indiana University, Bloomington, Indiana 47405, USA
c Universidad de Sevilla, Sevilla, Spain

Abstract: A triangulation of a surface with fixed topological type is called irreducible if no edge can be contracted to a vertex while remaining in the category of simplicial complexes and preserving the topology of the surface. A complete list of combinatorial structures of irreducible triangulations is made by hand for the once-punctured torus, consisting of exactly 297 non-isomorphic triangulations.

Keywords: triangulation of 2-manifold, irreducible triangulation, 2-manifold with boundary, punctured torus.

Funding Agency Grant Number
Ministerio de Ciencia e Innovación de España MTM 2010-20445
FQM-189
FQM-164
This work has been partially supported by P.A.I. Groups FQM-189, FQM-164 and MTM 2010-20445 (Government of Spain).


DOI: https://doi.org/10.17377/semi.2018.15.026

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Bibliographic databases:

Document Type: Article
UDC: 519.1
MSC: 57M15
Received March 5, 2016, published March 19, 2018
Language: English

Citation: S. Lawrencenko, T. Sulanke, M. T. Villar, L. V. Zgonnik, M. J. Chávez, J. R. Portillo, “Irreducible triangulations of the once-punctured torus”, Sib. Èlektron. Mat. Izv., 15 (2018), 277–304

Citation in format AMSBIB
\Bibitem{LawSulVil18}
\by S.~Lawrencenko, T.~Sulanke, M.~T.~Villar, L.~V.~Zgonnik, M.~J.~Ch\'avez, J.~R.~Portillo
\paper Irreducible triangulations of the once-punctured torus
\jour Sib. \`Elektron. Mat. Izv.
\yr 2018
\vol 15
\pages 277--304
\mathnet{http://mi.mathnet.ru/semr917}
\crossref{https://doi.org/10.17377/semi.2018.15.026}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000438412200026}


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