Geodesic
Irreducible triangulations of the once-punctured torus
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 277-304.

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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. 
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S. Lawrencenko; T. Sulanke; M. T. Villar; L. V. Zgonnik; M. J. Chávez; J. R. Portillo. Irreducible triangulations of the once-punctured torus. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 277-304. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a65/

[1] D. Barnette, “Generating the triangulations of the projective plane”, Journal of Combinatorial Theory, Series B, 33:3 (1982), 222–230 | DOI | MR

[2] D.W. Barnette, A.L. Edelson, “All 2-manifolds have finitely many minimal triangulations”, Israel Journal of Mathematics, 67:1 (1989), 123–128 | DOI | MR

[3] A. Boulch, É. Colin de Verdière, A. Nakamoto, “Irreducible triangulations of surfaces with boundary”, Graphs and Combinatorics, 29:6 (2013), 1675–1688 | DOI | MR

[4] R. Bowen, S. Fisk, “Generation of triangulations of the sphere”, Mathematics of Computation, 21 (1967), 250–252 | MR

[5] M.J. Chávez, S. Lawrencenko, J.R. Portillo, M.T. Villar, “An algorithm that constructs irreducible triangulations of once-punctured surfaces”, Proceedings of the XV Spanish Meeting on Computational Geometry (26–28 June 2013, Seville, Spain), eds. Díaz-Báñez J.M., Garijo D., Márquez A., Urrutia J., Prensa Universidad de Sevilla, Seville, 2013, 43–46 http://congreso.us.es/ecgeometry/proceedingsECG2013.pdf#page=51

[6] M.J. Chávez, S. Lawrencenko, J.R. Portillo, M.T. Villar, An algorithm that constructs irreducible triangulations of once-punctured surfaces, 31 August 2015, arXiv: 1410.7738

[7] M.J. Chávez, S. Lawrencenko, A. Quintero, M.T. Villar, Irreducible triangulations of the Möbius band, 15 June 2013, arXiv: 1306.3550

[8] M.J. Chávez, S. Lawrencenko, A. Quintero, M.T. Villar, “Irreducible triangulations of the Möbius band”, Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2 (2014), 44–50 | MR

[9] H. Edelsbrunner, J.L. Harer, Computational Topology: An Introduction, American Mathematical Society, Providence, RI, 2010 | MR

[10] B. Grünbaum, Convex Polytopes, Wiley, New York, 1967 | MR

[11] S. Lawrencenko, “Irreducible triangulations of the torus”, Journal of Mathematical Physics, Analysis, Geometry (Ukrainskii Geometricheskii Sbornik), 30 (1987), 52–62 (in Russian) | MR | Zbl

[12] S.A. Lavrenchenko, “Irreducible triangulations of the torus”, Journal of Mathematical Sciences (Journal of Soviet Mathematics), 51 (1990), 2537–2543 | MR

[13] S. Lawrencenko, Explicit lists of all automorphisms of the irreducible toroidal triangulations and of all toroidal embeddings of their labeled graphs, Report deposited at UkrNIINTI (Ukrainian Scientific Research Institute of Scientific and Technical Information), report No 2779-Uk87 (1 October 1987), Yangel Kharkov Institute of Radio Electronics, Kharkov, 1987 (in Russian)

[14] S. Lawrencenko, “Polyhedral suspensions of arbitrary genus”, Graphs and Combinatorics, 26:4 (2010), 537–548 | DOI | MR

[15] S. Lawrencenko, “Open problems on irreducible triangulations (invited lecture)”, Seminario de Geometría Diferencial y Topología (Department of Geometry and Topology, University of Seville, Seville, Spain, 22 May 2012) http://www.imus.us.es/images/stories/Actividades/2012/SEM_GT_05-22.pdf

[16] S. Lawrencenko, Geometric realization of toroidal quadrangulations without hidden symmetries, 3 July 2013, arXiv: 1307.1054 | MR

[17] S. Lawrencenko, “A tour around irreducible triangulations of surfaces (invited plenary lecture)”, The 25th Workshop on Topological Graph Theory conducted by Professors S. Negami and A. Nakamoto (22 November 2013, Yokohama National University, Yokohama, Japan) http://tgt.ynu.ac.jp/tgt25/tgt25program.pdf

[18] S. Lawrencenko, “Irreducible triangulations of 2-manifolds with boundary”, Proceedings of the Moscow Workshop on Combinatorics and Number Theory (27 January–2 February 2014, Dolgoprudny, Russia), eds. Raigorodskii A., Moshchevitin N., Moscow Institute of Physics and Technology, M., 2014, 24–26 http://mjcnt.phystech.edu/conference/moscow/speakers/lawrenchenko.pdf

[19] S. Lawrencenko, “Geometric realization of toroidal quadrangulations without hidden symmetries”, Geombinatorics, 24:1 (2014), 11–20 | MR

[20] S. Lawrencenko, S. Negami, “Irreducible triangulations of the Klein bottle”, Journal of Combinatorial Theory, Series B, 70:2 (1997), 265–291 | DOI | MR

[21] S. Lawrencenko, S. Negami, I.Kh. Sabitov, “A simpler construction of volume polynomials for a polyhedron”, Beiträge zur Algebra und Geometrie, 43:1 (2002), 261–273 | MR

[22] S. Lawrencenko, A.Yu. Shchikanov, “Euclidean realization of the product of cycles without hidden symmetries”, Siberian Electronic Mathematical Reports, 12 (2015), 777–783 (in Russian, English abstract) | MR

[23] S. Negami, “Diagonal flips in triangulations of surfaces”, Discrete Mathematics, 135:1–3 (1994), 225–232 | DOI | MR

[24] E. Steinitz, H. Rademacher, Vorlesungen über die Theorie der Polyeder unter Einschluss der Elemente der Topologie, reprint of the 1934 original German edition, Springer-Verlag, Berlin–Heidelberg–New York, 1976 | MR

[25] T. Sulanke, “Note on the irreducible triangulations of the Klein bottle”, Journal of Combinatorial Theory, Series B, 96:6 (2006), 964–972 | DOI | MR

[26] T. Sulanke, Generating irreducible triangulations of surfaces, 27 June 2006, arXiv: math/0606687

[27] T. Sulanke, Irreducible triangulations of low genus surfaces, 27 June 2006, arXiv: math/0606690

[28] T. Sulanke, Source for surftri and lists of irreducible triangulations, The Indiana University High Energy Physics Web, , 27 June 2006 http://hep.physics.indiana.edu/t̃sulanke/graphs/surftri/