Discrete geometry and convexity: in honour of Imre Barany: this special vol. is contributed by the speakers of the Discrete geometry and convexity conf., held in Budapest, June 19-23, 2017 / ed. by G.Ambrus et al. - Budapest: Alfred Renyi institute of mathematics, Hungarian academy of sciences, 2017. - 151 p.: ill. - Bibliogr. at the end of the art - ISBN 978-963-279-963-6 Шифр: (И/В18-D63) 02  Место хранения:   02 | Отделение ГПНТБ СО РАН | Новосибирск

Оглавление / Contents

Preface ......................................................... 9 A few great results of Imre Bárány ............................. 11 A few snapshots of Bárány ...................................... 14 Invited articles The beauty and the mystery of the symmetric moment curve ....... 19 Alexander Barvinok Monotonicity of functionals of random polytopes ................ 23 Mareen Beermann and Matthias Reitzner Thieves dividing birthday presents and birthday cakes .......... 29 Pavle Blagojević and Pablo Soberón Polynomials in finite geometry and combinatorics ............... 35 Aart Blokhuis Families of vectors without antipodal pairs .................... 38 Péter Frankl and Andrey Kupavskii On a Helly-type question for central symmetry .................. 44 Alexey Garber and Edgardo Roldán-Pensado An old method with two new geometrical applications ............ 50 Péter Hajnal and Endre Szemerédi Helly theorems for connected sets in the plane ................. 53 Andreas F. Holmsen Problems for Imre Bárány's Birthday ............................ 59 Gil Kalai Geometric representations and quantum physics .................. 66 László Lovász How small orbits of periodic homeomorphisms of spheres can be? ............................................................ 69 Luis Montejano and Evgeny V. Shchepin Random normal vectors are normal ............................... 74 Hoi H. Nguyen and Van H. Vu Families of curves with many touchings ......................... 82 János Pach and Géza Tóth k-monotone interpolation ....................................... 89 Attila Pór Polytopes and cones in random hyperplane tessellations ......... 91 Rolf Schneider Tensors, colors, and convex hulls .............................. 97 Pablo Soberón On the number of non-intersecting hexagons in 3-space ......... 102 József Solymosi and Ching Wong A vector-sum theorem and the Fermat-Torricelli problem in normed planes ................................................. 106 Konrad J. Swanepoel Holes in planar point sets .................................... 111 Pavel Valtr F-convexity: A short survey ................................... 114 Liping Yuan and Tudor Zamfirescu Contributed articles Algebraic vertices of non-convex polyhedra .................... 123 Arseniy Akopyan Longest convex chains and subadditive ergodicity .............. 125 Gergely Ambrus Random polytopes and the affine surface area .................. 127 Károly J. Böröczky Random approximations of convex bodies by ball-polytopes ...... 133 Ferenc Fodor Globalizing groups ............................................ 135 Augustin Fruchard А note on a picture-hanging puzzle ............................ 137 Radoslav Fulek Coin-weighting and different directions of lines .............. 138 Zoltán Füredi Proof of László Fejes Tóth's zone conjecture .................. 142 Zilin Jiang and Alexandr Polyanskii Dense regular horoball packings in higher dimensional hyperbolic spaces ............................................. 143 Robert Thijs Kozma Approximation of convex bodies by polytopes in the geometric distance ...................................................... 145 Márton Naszódi On the gap between translative and lattice kissing numbers of a convex body .............................................. 148 István Talata A result in asymmetric Euclidean Ramsey theory ................ 149 Sergei Tsaturian On the geometry of Alexandrov surfaces ........................ 150 Costin Vilcu