Polytopes
1. Ordinary 3-polytopes, Geometriae Dedicata, 52(1994), 129-142.
2. On a class of generalized simplices, Mathematika, 43(1996), 274-285.
3. Ordinary (2m + 1) -polytopes, Israel J. of Mathematics, 102(1997), 101-123.
4. with G. Karolyi, Subpolytopes of cyclic polytopes, Eur. J. Comb., 21(2000), 13-17.
5. with K. Boroczky jr., Oriented matroid rigidity of multiplices , Discrete Comput. Geom., 24(2000), 177-184.
6. On sewing neighbourly polytopes, Note di Matematica, 20(2000/2001), 73-80.
7. A construction for periodically-cyclic Gale 2m-polytopes, Beitraege zur Alg. und Geom., 42(2001), 89-101.
8. A class of periodically-cyclic 6-polytopes, U. of Calgary, Dept. of Math and Stat. Research Paper # 814, (2001). 23pp.
9. with K. Boroczky, jr., On periodically-cyclic Gale 4-polytopes, Discr. Math., 241(2001), 103-118.
10. A class of four dimensional Gale polytopes, U. of Calgary, Dept. of Math. and Stat. Research Paper #821, (2001), 14pp.
11. Separation in neighbourly 4-polytopes, Stud. Sci, Math. Hung. , 39 (2002), 277-289.
12. with D. Oliveros, Separation in totally-sewn 4-polytopes, Discrete Mathematics.,253(2003), 59-68.
13. with K. Boroczky jr. and D. S. Gunderson, Cyclic polytopes, hyperplanes and Gray codes, J. of Geometry, 76 (2003), 25-49.
14. with K. Bezdek and K. Boroczky, Edge-antipodal 3-polytopes, Combinatorial and Computational Geomety, MSRI Publ. 52, (2005) 129-134.
15. with K Boroczky, On antipodal 3-polytopes, Rom. J. Pure Appl. Math., 50 (2005),477-481.
16. Characterizations of cyclic polytopes, J. of Geometry , 84 (2005),30-36 .
17. with M. Bayer, On Gale and braxial polytopes , Arch. Math., 89 (2007) ,373-384.
18. with M. Bayer, On braxtopes , a class of generalized simplices, Beitraege zur Alg. und Geom., 49 (2008), 137-145.
19. with K. Boroczky, On edge-antipodal d-polytopes, Per. Math. Hungarica, 57 (2008),13-23.
20. with K. Boroczky, F. Fodor, A. Heppes and D. Oliveros, Centred subpolytopes of the 4-cube, U. of Calgary, Dept. of Math. and Stat. Research Paper #862 (2010), 13pp.
21. with F. Fodor and D. Oliveros, Separation in totally-sewn 4-polytopes with the decreasing universal edge property,Beitraege Math. und Alg., 53 (2012), 123-138.
22. with J. Lawrence, Combinatorial types of Bi-cyclic 4-polytopes, Discrete Mathematics, 312 (2012), 1863-1876.
23. Separation in Convex Polytopes, CMS Notes, 45(1), February 2013 ,14.
24. with F. Fodor, A separation theorem for totally-sewn 4-polytopes, Studia Math. Hungarica, 52(3),(2015),386-422.
25. Separation in Simply Linked Neighbourly 4-polytopes. arXiv:1703.03803v1(2017),19 pp.
26. with D. Oliveros, d-dimensional self-dual polytopes and Meissner polytopes, AMS Contemporary Mathematics:Polytopes and Discrete Geometry, Vol. 764 (2021),21-30, https://doi.org/10.1090/conm/764/15357 .
27. with G. Lopez-Campos and D. Oliveros, Configured polytopes and extremal configurations, Ars Math. Contemp. (2022), https://doi.org/10.26493/1855-3974.2559.e4f.
28. A combinatorial construction of bi-cyclic 4-polytopes. Studia Math. Hungarica, 61(1),(2024), 73-87.
29. Generalizations of cyclic polytopes. arXiv:2405.094299v2(2024),10 pp.
Discrete and Combinatorial Geometry
1. with G. Fejes Toth, A generalization of the Erdos-Szekeres convex n – gon theorem, J. reine angew. Math., 395 (1989), 167-170.
2. with C. Fejes Toth, Nine convex sets determine a pentagon with convex sets as vertices, Geometriae Dedicata, 31 (1989), 89-104.
3. with G. Fejes Toth, Convexly independent sets, Combinatorics, 10 (1990), 195-202.
4. with K. Boroczky, jr, H. Harborth and L. Piepmeyer, On the smallest limited snake of unit disks, Geometria Dedicata, 40 (1991), 319-324.
5. with A. Bezdek and K. Bezdek, On the (n – 2)-transversals of n convex subsets of the plane, Geometriae Dedicata, 40 (1991), 263-268.
6. with A. Bezdek and K. Bezdek, On illumination in the plane by line segments, Geometriae Dedicata, 41(1992), 39-50.
7. with K. Bezdek, Hadwiger’s covering conjecture and low dimensional dual cyclic poly-topes, Geometriae Dedicata, 46(1993, 279-286.
8. with V. Soltan, Some Erdos-Szekeres type results about points in space, Monatshaft fur Mathematik, 118(1994), 33-40.
9. with H. Harborth, On empty convex polytopes, J. of Geometry, 52(1995), 25-29.
10. with K. Bezdek, A proof of Hadwiger’s Conjecture for dual cyclic polytopes, Geometriae Dedicata, 68(1997), 29-41.
11. with H. Harborth, Smallest limited edge-to-edge snakes in Euclidean Tessalations,Congressus Numeratium, 149(2001), 155-159.
12. with G. Fejes Toth, The Erdos-Szekeres problem for planar points in arbitrary position, Discrete Math., 253 (2003), 49-58.
13. A signature theorem for uniform matroids, U. of Calgary, Dept. of Math. and Stat. Research Paper #840 (2004), 10pp.
14. with K. Hosono, Gy. Karolyi and M. Urabe, Constructions from empty polygons, Per. Math. Hungarica., 49 (2004), 1-8.
15. with. F. Fodor and D. Oliveros, Large transversals to families of unit disks, Acta. Math. Hungarica., 106(2005), 285-291.
16. with F. Fodor and D. Oliveros, A transversal property of families of eight or nine unit disks, Bol. Soc. Math. Mex., 12 (2006),59-73.
17. with K. Bezdek, B. Csikos and A. Heppes, On the transversal Helly numbers of disjoint and overlapping disks, Arch. Math.,87 (2006), 86-96.
18. with A. Bezdek, Incenter iterations in the Plane and on the Sphere, Proc. Int. Conf.( Comm: Algebra and Combinatorics), 4 (2007),1-6.
19. with F. Fodor and D. Oliveros, The T(4) property of families of unit disks, Israel J. Math.,168(2008), 239-252.
20. with K. Boroczky and A. Heppes, T(5) Families of overlapping disks, Acta Math Hungarica, 142(1), (2014), 31-55.
21. with A. Bezdek, Finding equal-diameter triangulations in polygons, Beitraege Math. und Alg. (2014), online DOI:10.1007/s13366-014-0206-6.
22. with K. Boroczky and K.J. Boroczky, The T(5) property of packing of squares, The Art of Discrete and Applied Mathematics,Vol.4,No.3,(2021),https://doi.org/10.26493/2590-9770.1336.1e0.
Order and Convex Geometry
1. Hypersurfaces of Order Two, A.M.S. Trans., 220 (1976), 205-233.
2. Surfaces of Order Three with a Peak I, J. of Geometry, 11/1(1978), 55-83.
3. Surfaces of Order Three with a Peak II, J. of Geometry, 11/2(1978), 110-138.
4. Biplanar Surfaces of Order Three, Canad. J. of Math., 31 (1979), 396-418.
5. Uniplanar Surfaces of Order Three, Geometriae Dedicata, 8 (1979), 259-277.
6. On Surfaces of Order Three, Canad. Math. Bull., 22/3(1979), 351-355.
7. On the Lines of a Surface of Order Three, Math. Ann., 243 (1979), 191-195.
8. Biplanar Surfaces of Order Three, II, Canad. J. of Math., 32 (1980), 839-866.
9. with I. Rival, Continuous, Slope-preserving Maps of simple Closed Curves, Canad. J. of Math., 32 (1980), 1102-1113.
10. C-nodal Surfaces of Order Three Canad. J. of Math., 25 (1983), 68-100.
11. On the singularities of almost-simple plane curves, Pac. J. Math., 109 (1983), 257-273.
12. with P. Scherk, An application of a theorem by Hjelmslev, C.R. Math. Rep. Acad. Sci. Canada, 5 (1983), 195-199.
13. Inflectional convex space curves, Can. J. of Math. 36 (1984), 537-549.
14. with P. Scherk, A property of arcs of order n in R, C.R. Math. Rep. Acad. Sci. Canada, 6 (1984), 165-170.
15. On the singularities of simple plane curves, Michigan Math. J., 32 (1985), 141-151.
16. with P. Scherk, Ordinary arcs on convex bodies, C.R. Math. Rep. Acad. Sci. Canada, 7 (1985), 27-32.
17. An n-vertex theorem for convex space curves, Canad. J. Math., 37 (1985), 217-237.
18. with P. Scherk, A geometric characterization of arcs of order n in R, C.R. Math. Rep. Acad. Sci. Canada, 7 (1985), 303-308.
19. with J. Schaer, On convex space curves, C.R. Math. Rep. Acad. Sci. Canada, 7 (1985), 369-374.
20. On the singularities of plane curves, Canad. J. of Math., 38 (1986), 947-968.
21. On the four-vertex theorem for space curves, J. of Geometry, 27 (1986), 166-174.
22. On inflectional space curves with four vertices, C.R. Math. Rep. Acad. Sci. Canada 8 (1986), 225-230.
23. On inflectional space curves with four vertices II, C.R. Math. Rep. Acad. Sci. Canada 8 (1986), 277-282.
24. with J. Schaer, Linearly related plane convex sets, Intuitive Geometry, Pap. mt. Conf. Si6fok, Hungary, 1985, Colloq. Math. Soc. Janos Bolyai, 48 (1987), 167-177.
25. with J. Schaer, Affinely embeddable convex sets, Acta. Math. Hung, 49 (1987), 353- 363.
26. Some examples in projective convexity, C.R. Math. Rep. Acad. Sci. Canada, 9 (1987), 199-204.
27. with J. Pach, An upper bound for families of linearly related plane convex sets, Arch. Math., 50 (1988), 56-58.
28. Affinely embeddable convex bodies, Geometriae Dedicata, 26 (1988), 99-109.
29. Convex sets and plane curve singularities, J. of Geometry, 34 (1989), 14-29.
30. On separated families of convex bodies, Arch. der Math., 54 (1990), 193-199.
31. with K. Bezdek and R. Connelly, On hyperplanes and polytopes, Monatshefte fur Math., 109 (1990), 39-48.
32. Affinely embeddable separated families, Arch. der Math., 55 (1990), 400-406.
33. with K. Boroczky, jr., About the centroid body and the ellipsoid of inertia, Mathematika,48 (2001), 1-14.
Incidence Geometry
1. with J.W. Lorimer, Axiom systems for Affine Klingenberg Spaces, Proc. mt. Conf. Combinatorics 88, Ravello, Italy (1991), 185-200,
2. with J.W. Lorimer, On hyperplanes and free subspaces of affine Klingenberg spaces, Aequationes Mathematicae, 48(1994), 121-136.
3. with J.W. Lorimer, Subspace operations in affine Klingenberg spaces, Bulletin of Belgian Mathematical Society, 2(1995), 99-108.
4. with J.W. Lorimer, Homomorphisms of affine spaces, Abh. Math. Sem. Universitat Hamburg, 65(1995), 283-292.
5. with J. W. Lorimer, Translations in Affine Klingenberg Spaces, J. of Geometry, 99(2010),15-42 .
Books and Journals Edited
POLYTOPES: Abstract, Convex and Computational
NATO ASI SERIES C: Mathematical and Physical Sciences, Volume 440, (1994), 507 pp.
Kluwer Academic Publishers
Editors: T. Bisztriczky, P. McMullen, R. Schneider, A.I. Weiss.
DISCRETE GEOMETRY, Periodica Mathematica Hungarica, 53(1-2), 2006
Guest Editors: T. Bisztriczky, F. Fodor and W. Kuperberg
This special volume is dedicated to K. Bezdek and consists primarily of articles presented at the following meetings in Calgary and Banff :
– Calgary Workshop in Discrete Geometry, U. of Calgary, May 13-14, 2005.
– Densest Packing of Spheres, BIRS, May 14-19, 2005.
– Convex and Abstract Polytopes,BIRS, May 19 – 21, 2005.
– Polytopes Day in Calgary, U. of Calgary, May 22, 2005.
INTUITIVE GEOMETRY, Periodica Mathematica Hungarica, 57(2), 2008.
Guest Editors: T. Bisztriczky,G. Fejes Toth, F. Fodor and W. Kuperberg
This special volume is dedicated to A. Bezdek and consists primarily of articles presented at the following meetings in Calgary and Banff:
-Intuitive Geometry Workshop, BIRS, Aug.31-Sept.2, 2007.
-Intuitive Geometry Day in Calgary, U.of Calgary, Sept.3, 2007.
Coming Attractions
1. with G. Fejes Toth, An Erdos-Szekeres theorem for planar convex sets.
2. Generalizations of cyclic polytopes.
Lecture Videos
Erdos-Szekeres type theorems for planar convex sets.
Retrospective Workshop on Discrete Geometry, Optimization and Symmetry, November 25-29, 2013.
http://www.fields.utoronto.ca/video-archive/2013/11/238-2607
Transversal problems for phi-disjoint ovals.
Transversal, Helly and Tverberg type Theorems in Geometry, Combinatorics and Topology III , October 23-27,2016.
https://open.library.ubc.ca/cIRcle/collections/48630/items/1.0348140
Links ( Publication Content)
https://www.researchgate.net/profile/T_Bisztriczky/publications
http://www.ams.org/mathscinet/MRAuthorID/37375
