Main Branches

Downloads  Installation  Overview  Data Libraries  Packages  Documentation  Contacts  FAQ  GAP 3 

101 publications using GAP in the category "Convex and discrete geometry"

[ABL17] Adiprasito, K. A., Benedetti, B., and Lutz, F. H., Extremal examples of collapsible complexes and random discrete Morse theory, Discrete Comput. Geom., 57 (4) (2017), 824–853.

[AGL14] Akiyama, S., Gähler, F., and Lee, J., Determining pure discrete spectrum for some self-affine tilings, Discrete Math. Theor. Comput. Sci., 16 (3) (2014), 305–316.

[AC+05] Artal Bartolo, E., Carmona Ruber, J., Cogolludo-Agustín, J. I., and Marco Buzunáriz, M., Topology and combinatorics of real line arrangements, Compos. Math., 141 (6) (2005), 1578–1588.

[BD12] Bagchi, B. and Datta, B., A triangulation of $\Bbb CP^3$ as symmetric cube of $S^2$, Discrete Comput. Geom., 48 (2) (2012), 310–329.

[B99] Bailey, G. D., Coherence and enumeration of tilings of $3$-zonotopes, Discrete Comput. Geom., 22 (1) (1999), 119–147.

[BB+09] Ballinger, B., Blekherman, G., Cohn, H., Giansiracusa, N., Kelly, E., and Schürmann, A., Experimental study of energy-minimizing point configurations on spheres, Experiment. Math., 18 (3) (2009), 257–283.

[BC12] Barakat, M. and Cuntz, M., Coxeter and crystallographic arrangements are inductively free, Adv. Math., 229 (1) (2012), 691–709.

[BH+09] Baumeister, B., Haase, C., Nill, B., and Paffenholz, A., On permutation polytopes, Adv. Math., 222 (2) (2009), 431–452.

[BM+14] Berman, L. W., Mixer, M., Monson, B., Oliveros, D., and Williams, G., The monodromy group of the $n$-pyramid, Discrete Math., 320 (2014), 55–63.

[BM+15] Berman, L. W., Monson, B., Oliveros, D., and Williams, G. I., The monodromy group of a truncated simplex, J. Algebraic Combin., 42 (3) (2015), 745–761.

[BM+18] Berman, L. W., Monson, B., Oliveros, D., and Williams, G. I., Fully truncated simplices and their monodromy groups, Adv. Geom., 18 (2) (2018), 193–206.

[BD+13] Bishop, M., Douglass, J. M., Pfeiffer, G., and Röhrle, G., Computations for Coxeter arrangements and Solomon's descent algebra II: Groups of rank five and six, J. Algebra, 377 (2013), 320–332.

[BD+15] Bishop, M., Douglass, J. M., Pfeiffer, G., and Röhrle, G., Computations for Coxeter arrangements and Solomon's descent algebra III: Groups of rank seven and eight, J. Algebra, 423 (2015), 1213–1232.

[BN19] Bogya, N. and Nagy, G. P., Light dual multinets of order six in the projective plane, Acta Math. Hungar., 159 (2) (2019), 520–536.

[BKP19] Bojarski, J., Kisielewicz, A., and Przesławski, K., Nearly neighbourly families of standard boxes, Electron. J. Combin., 26 (4) (2019), Paper No. 4.44, 39.

[BG+96] Bokowski, J., Guedes de Oliviera, A., Thiemann, U., and Veloso da Costa, A., On the cube problem of Las Vergnas, Geom. Dedicata, 63 (1) (1996), 25–43.

[BD+14] Bremner, D., Dutour Sikirić, M., Pasechnik, D. V., Rehn, T., and Schürmann, A., Computing symmetry groups of polyhedra, LMS J. Comput. Math., 17 (1) (2014), 565–581.

[BGM21] Bruns, W., García-Sánchez, P. A., and Moci, L., The monoid of monotone functions on a poset and quasi-arithmetic multiplicities for uniform matroids, J. Algebra, 569 (2021), 377–400.

[CT16] Caroli, M. and Teillaud, M., Delaunay triangulations of closed Euclidean $d$-orbifolds, Discrete Comput. Geom., 55 (4) (2016), 827–853.

[C05] Cochet, C., Kostka numbers and Littlewood-Richardson coefficients, in Integer points in polyhedra—geometry, number theory, algebra, optimization, Amer. Math. Soc., Providence, RI, Contemp. Math., 374 (2005), 79–89.

[C02] Cousineau, G., Tilings as a programming exercise, Theoret. Comput. Sci., 281 (1-2) (2002), 207–217
(Selected papers in honour of Maurice Nivat).

[C12] Cunningham, G., Mixing chiral polytopes, J. Algebraic Combin., 36 (2) (2012), 263–277.

[C12] Cunningham, G., Mixing regular convex polytopes, Discrete Math., 312 (4) (2012), 763–771.

[CP14] Cunningham, G. and Pellicer, D., Chiral extensions of chiral polytopes, Discrete Math., 330 (2014), 51–60.

[DLM10] Dai Pra, P., Louis, P., and Minelli, I. G., Realizable monotonicity for continuous-time Markov processes, Stochastic Process. Appl., 120 (6) (2010), 959–982.

[DS13] Datta, B. and Singh, N., An infinite family of tight triangulations of manifolds, J. Combin. Theory Ser. A, 120 (8) (2013), 2148–2163.

[DJS11] D'Azevedo, A. B., Jones, G. A., and Schulte, E., Constructions of chiral polytopes of small rank, Canad. J. Math., 63 (6) (2011), 1254–1283.

[DH99] Delgado Friedrichs, O. and Huson, D. H., Tiling space by Platonic solids. I, Discrete Comput. Geom., 21 (2) (1999), 299–315.

[DH00] Delgado Friedrichs, O. and Huson, D. H., 4-regular vertex-transitive tilings of $\bold E^3$, Discrete Comput. Geom., 24 (2-3) (2000), 279–292
(The Branko Grünbaum birthday issue).

[DEJ14] Derenthal, U., Elsenhans, A., and Jahnel, J., On the factor alpha in Peyre's constant, Math. Comp., 83 (286) (2014), 965–977.

[DM12] Donten-Bury, M. and Michałek, M., Phylogenetic invariants for group-based models, J. Algebr. Stat., 3 (1) (2012), 44–63.

[DFM04] Dougherty, R., Faber, V., and Murphy, M., Unflippable tetrahedral complexes, Discrete Comput. Geom., 32 (3) (2004), 309–315.

[D04] Dutour, M., The six-dimensional Delaunay polytopes, European J. Combin., 25 (4) (2004), 535–548.

[DD04] Dutour, M. and Deza, M., Goldberg-Coxeter construction for 3- and 4-valent plane graphs, Electron. J. Combin., 11 (1) (2004), Research Paper 20, 49.

[DER07] Dutour, M., Erdahl, R., and Rybnikov, K., Perfect Delaunay polytopes in low dimensions, Integers, 7 (2007), A39, 49.

[D17] Dutour Sikirić, M., The seven dimensional perfect Delaunay polytopes and Delaunay simplices, Canad. J. Math., 69 (5) (2017), 1143–1168.

[DGM20] Dutour Sikirić, M., Garber, A., and Magazinov, A., On the Voronoi conjecture for combinatorially Voronoi parallelohedra in dimension 5, SIAM J. Discrete Math., 34 (4) (2020), 2481–2501.

[DIP07] Dutour Sikirić, M., Itoh, Y., and Poyarkov, A., Cube packings, second moment and holes, European J. Combin., 28 (3) (2007), 715–725.

[DSV10] Dutour Sikirić, M., Schürmann, A., and Vallentin, F., The contact polytope of the Leech lattice, Discrete Comput. Geom., 44 (4) (2010), 904–911.

[E09] Edmonds, A. L., The partition problem for equifacetal simplices, Beiträge Algebra Geom., 50 (1) (2009), 195–213.

[E11] Effenberger, F., Stacked polytopes and tight triangulations of manifolds, J. Combin. Theory Ser. A, 118 (6) (2011), 1843–1862.

[EK10] Effenberger, F. and Kühnel, W., Hamiltonian submanifolds of regular polytopes, Discrete Comput. Geom., 43 (2) (2010), 242–262.

[FP20] Fernandes, M. E. and Piedade, C. A., Faithful permutation representations of toroidal regular maps, J. Algebraic Combin., 52 (3) (2020), 317–337.

[FL16] Friese, E. and Ladisch, F., Affine symmetries of orbit polytopes, Adv. Math., 288 (2016), 386–425.

[GHK13] Gähler, F., Hunton, J., and Kellendonk, J., Integral cohomology of rational projection method patterns, Algebr. Geom. Topol., 13 (3) (2013), 1661–1708.

[GTV03] Garber, D., Teicher, M., and Vishne, U., $\pi_1$-classification of real arrangements with up to eight lines, Topology, 42 (1) (2003), 265–289.

[GLD18] Gomi, Y., Loyola, M. L., and De Las Peñas, M. L. A. N., String C-groups of order 1024, Contrib. Discrete Math., 13 (1) (2018), 1–22.

[G11] Gonçalves, D., On the $K$-theory of the stable $C^*$-algebras from substitution tilings, J. Funct. Anal., 260 (4) (2011), 998–1019.

[H03] Hartley, M. I., Quotients of some finite universal locally projective polytopes, Discrete Comput. Geom., 29 (3) (2003), 435–443.

[H05] Hartley, M. I., Locally projective polytopes of type $\4,3,\dots,3,p\$, J. Algebra, 290 (2) (2005), 322–336.

[H06] Hartley, M. I., An atlas of small regular abstract polytopes, Period. Math. Hungar., 53 (1-2) (2006), 149–156.

[H06] Hartley, M. I., Simpler tests for semisparse subgroups, Ann. Comb., 10 (3) (2006), 343–352.

[H08] Hartley, M. I., An exploration of locally projective polytopes, Combinatorica, 28 (3) (2008), 299–314.

[H10] Hartley, M. I., Covers $\scr P$ for abstract regular polytopes $\scr Q$ such that $\scr Q=\scr P/\bf Z^k_p$, Discrete Comput. Geom., 44 (4) (2010), 844–859.

[H11] Hartley, M. I., Eulerian abstract polytopes, Aequationes Math., 82 (1-2) (2011), 1–23.

[HH10] Hartley, M. I. and Hulpke, A., Polytopes derived from sporadic simple groups, Contrib. Discrete Math., 5 (2) (2010), 106–118.

[HL04] Hartley, M. I. and Leemans, D., Quotients of a universal locally projective polytope of type $\5,3,5\$, Math. Z., 247 (4) (2004), 663–674.

[HL09] Hartley, M. I. and Leemans, D., On locally spherical polytopes of type $\5,3,5\$, Discrete Math., 309 (1) (2009), 247–254.

[HMS00] Hausel, T., Makai Jr. , E., and Szűcs, A., Inscribing cubes and covering by rhombic dodecahedra via equivariant topology, Mathematika, 47 (1-2) (2000), 371–397 (2002).

[HRS15] Herr, K., Rehn, T., and Schürmann, A., On lattice-free orbit polytopes, Discrete Comput. Geom., 53 (1) (2015), 144–172.

[HJ+09] Herrmann, S., Jensen, A., Joswig, M., and Sturmfels, B., How to draw tropical planes, Electron. J. Combin., 16 (2, Special volume in honor of Anders Björner) (2009), Research Paper 6, 26.

[HR16] Hoge, T. and Röhrle, G., Nice reflection arrangements, Electron. J. Combin., 23 (2) (2016), Paper 2.9, 24.

[HL07] Hohlweg, C. and Lange, C. E. M. C., Realizations of the associahedron and cyclohedron, Discrete Comput. Geom., 37 (4) (2007), 517–543.

[HP04] Hood, J. and Perkinson, D., Some facets of the polytope of even permutation matrices, Linear Algebra Appl., 381 (2004), 237–244.

[IJM20] Iverson, J. W., Jasper, J., and Mixon, D. G., Optimal line packings from nonabelian groups, Discrete Comput. Geom., 63 (3) (2020), 731–763.

[KK03] Kimmerle, W. and Kouzoudi, E., Doubly transitive automorphism groups of combinatorial surfaces, Discrete Comput. Geom., 29 (3) (2003), 445–457.

[KL99] Kühnel, W. and Lutz, F. H., A census of tight triangulations, Period. Math. Hungar., 39 (1-3) (1999), 161–183
(Discrete geometry and rigidity (Budapest, 1999)).

[L16] Ladisch, F., Realizations of abstract regular polytopes from a representation theoretic view, Aequationes Math., 90 (6) (2016), 1169–1193.

[LS18] Ladisch, F. and Schürmann, A., Equivalence of lattice orbit polytopes, SIAM J. Appl. Algebra Geom., 2 (2) (2018), 259–280.

[LST01] Lempken, W., Schröder, B., and Tiep, P. H., Symmetric squares, spherical designs, and lattice minima, J. Algebra, 240 (1) (2001), 185–208
(With an appendix by Christine Bachoc and Tiep).

[L08] Long, C., Small volume closed hyperbolic 4-manifolds, Bull. Lond. Math. Soc., 40 (5) (2008), 913–916.

[L99] Lutz, F. H., Triangulated manifolds with few vertices and vertex-transitive group actions, Verlag Shaker, Aachen, Berichte aus der Mathematik. [Reports from Mathematics] (1999), vi+137 pages
(Dissertation, Technischen Universität Berlin, Berlin, 1999).

[L02] Lutz, F. H., Examples of $\Bbb Z$-acyclic and contractible vertex-homogeneous simplicial complexes, Discrete Comput. Geom., 27 (1) (2002), 137–154
(Geometric combinatorics (San Francisco, CA/Davis, CA, 2000)).

[L08] Lutz, F. H., Combinatorial 3-manifolds with 10 vertices, Beiträge Algebra Geom., 49 (1) (2008), 97–106.

[M09] Marco Buzunáriz, M. Á., A description of the resonance variety of a line combinatorics via combinatorial pencils, Graphs Combin., 25 (4) (2009), 469–488.

[M14] McMullen, P., Realizations of regular polytopes, IV, Aequationes Math., 87 (1-2) (2014), 1–30.

[MPW12] Monson, B., Pellicer, D., and Williams, G., The tomotope, Ars Math. Contemp., 5 (2) (2012), 355–370.

[MPW14] Monson, B., Pellicer, D., and Williams, G., Mixing and monodromy of abstract polytopes, Trans. Amer. Math. Soc., 366 (5) (2014), 2651–2681.

[MP+07] Monson, B., Pisanski, T., Schulte, E., and Weiss, A. I., Semisymmetric graphs from polytopes, J. Combin. Theory Ser. A, 114 (3) (2007), 421–435.

[MS04] Monson, B. and Schulte, E., Reflection groups and polytopes over finite fields. I, Adv. in Appl. Math., 33 (2) (2004), 290–317.

[MS07] Monson, B. and Schulte, E., Reflection groups and polytopes over finite fields. II, Adv. in Appl. Math., 38 (3) (2007), 327–356.

[MS10] Monson, B. and Schulte, E., Locally toroidal polytopes and modular linear groups, Discrete Math., 310 (12) (2010), 1759–1771.

[MS12] Monson, B. and Schulte, E., Semiregular polytopes and amalgamated C-groups, Adv. Math., 229 (5) (2012), 2767–2791.

[MS14] Monson, B. and Schulte, E., Finite polytopes have finite regular covers, J. Algebraic Combin., 40 (1) (2014), 75–82.

[MS20] Monson, B. and Schulte, E., The assembly problem for alternating semiregular polytopes, Discrete Comput. Geom., 64 (2) (2020), 453–482.

[MW07] Monson, B. and Weiss, A. I., Medial layer graphs of equivelar 4-polytopes, European J. Combin., 28 (1) (2007), 43–60.

[P17] Pasechnik, D. V., Locally toroidal polytopes of rank 6 and sporadic groups, Adv. Math., 312 (2017), 459–472.

[PH18] Pedersen, M. C. and Hyde, S. T., Polyhedra and packings from hyperbolic honeycombs, Proc. Natl. Acad. Sci. USA, 115 (27) (2018), 6905–6910.

[P10] Pellicer, D., A construction of higher rank chiral polytopes, Discrete Math., 310 (6-7) (2010), 1222–1237.

[P14] Pellicer, D., Vertex-transitive maps with Schläfli type $\3,7\$, Discrete Math., 317 (2014), 53–74.

[PB14] Plesken, W. and Bächler, T., Counting polynomials for linear codes, hyperplane arrangements, and matroids, Doc. Math., 19 (2014), 285–312.

[R03] Reid, M., Tile homotopy groups, Enseign. Math. (2), 49 (1-2) (2003), 123–155.

[S10] Schürmann, A., Perfect, strongly eutactic lattices are periodic extreme, Adv. Math., 225 (5) (2010), 2546–2564.

[S11] Spreer, J., Normal surfaces as combinatorial slicings, Discrete Math., 311 (14) (2011), 1295–1309.

[S12] Spreer, J., Partitioning the triangles of the cross polytope into surfaces, Beitr. Algebra Geom., 53 (2) (2012), 473–486.

[SK11] Spreer, J. and Kühnel, W., Combinatorial properties of the $K3$ surface: simplicial blowups and slicings, Exp. Math., 20 (2) (2011), 201–216.

[S01] Suciu, A. I., Fundamental groups of line arrangements: enumerative aspects, in Advances in algebraic geometry motivated by physics (Lowell, MA, 2000), Amer. Math. Soc., Providence, RI, Contemp. Math., 276 (2001), 43–79.

[S02] Suciu, A. I., Translated tori in the characteristic varieties of complex hyperplane arrangements, Topology Appl., 118 (1-2) (2002), 209–223
(Arrangements in Boston: a Conference on Hyperplane Arrangements (1999)).

[T08] Timofeenko, A. V., Non-Platonic and non-Archimedean noncomposite polyhedra, Fundam. Prikl. Mat., 14 (2) (2008), 179–205.

[UTM14] Upadhyay, A. K., Tiwari, A. K., and Maity, D., Semi-equivelar maps, Beitr. Algebra Geom., 55 (1) (2014), 229–242.

[WB04] Wilson, S. and Breda d'Azevedo, A., Surfaces having no regular hypermaps, Discrete Math., 277 (1-3) (2004), 241–274.