Library of Triangulations swMATH ID: 20482 Software Authors: Bruno Benedetti, Frank H. Lutz Description: Random discrete Morse theory and a new library of triangulations. The discrete Morse theory, as defined by R. Forman, is used in a random algorithm. This means that the function is chosen randomly, and then the number of critical points is calculated leading to the random discrete Morse vector (c 0 ,⋯,c d ). This is considered as a kind of measuring the complexity of the triangulation. The discrete Morse vector can be much larger than the Betti vector but it turns out that in many cases the random Morse function produces the optimal Morse vector, i.e., the function is perfect. This is illustrated by numerous computer experiments with 10.000 choices of Morse functions on concrete triangulations of certain manifolds with a number of vertices ranging between 8 and several thousands. Typically most of the functions were perfect, in some cases more than 90 Homepage: http://page.math.tu-berlin.de/~lutz/stellar/library_of_triangulations/ Related Software: Simplicial complex library; RedHom; polymake; CHomP; Perseus; GAP; SageMath; plantri; ChainCon; CAPD; R; DiscreteMorse; LibTW; GitHub; simpcomp; Regina; FundamentalGroup; BISTELLAR Cited in: 14 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year Random discrete Morse theory and a new library of triangulations. Zbl 1296.57018Benedetti, Bruno; Lutz, Frank H. 2014 all top 5 Cited by 23 Authors 5 Lutz, Frank Hagen 4 Benedetti, Bruno 2 Newman, Andrew F. 1 Adiprasito, Karim Alexander 1 Bac, Alexandra 1 Burton, Benjamin A. 1 Casali, Maria Rita 1 Cristofori, Paola 1 Gonzalez-Lorenzo, Aldo 1 Kahle, Matthew 1 Kang, Mihyun 1 Lewiner, Thomas 1 Lofano, Davide 1 Mari, Jean-Luc 1 Møller, Jesper Michael 1 Paixão, João 1 Paolini, Giovanni 1 Parsons, Kyle 1 Real, Pedro 1 Spreer, Jonathan 1 Sprussel, Philipp 1 Tancer, Martin 1 Venturello, Lorenzo all top 5 Cited in 8 Serials 4 The Electronic Journal of Combinatorics 3 Discrete & Computational Geometry 2 Experimental Mathematics 1 Israel Journal of Mathematics 1 Nuclear Physics. B 1 Beiträge zur Algebra und Geometrie 1 ACM Transactions on Mathematical Software 1 Topology and its Applications all top 5 Cited in 7 Fields 10 Manifolds and cell complexes (57-XX) 8 Combinatorics (05-XX) 6 Convex and discrete geometry (52-XX) 4 Algebraic topology (55-XX) 4 Computer science (68-XX) 1 Probability theory and stochastic processes (60-XX) 1 Relativity and gravitational theory (83-XX) Citations by Year