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, 78 (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.
Honours
Geometry Fest, Conference in honour of 60’th birthday of T. Bisztriczky, Renyi Institute of Mathematics, Budapest, June 2007.
Canadian Mathematical Bulletin, 52(3), Issue dedicated to T. Bisztriczky, September 2009.
Discrete Geometry Fest, Conference in honour of T. Bisztriczky, G. Fejes Toth and E. Makai, Renyi Institute of Mathematics, Budapest, June 2017.
Coming Attractions
1. with G. Fejes Toth, An Erdos-Szekeres theorem for planar convex sets.
2. A second combinatorial construction of bi-cyclic 4-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
