Polytopes and Discrete Geometry

ISBN-13: 9781470448974

Gabriel Cunningham;Mark Mixer;Egon Schulte

Opis

This volume contains the proceedings of the AMS Special Session on Polytopes and Discrete Geometry, held from April 21-22, 2018, at Northeastern University, Boston, Massachusetts. The papers showcase the breadth of discrete geometry through many new methods and results in a variety of topics. Also included are survey articles on some important areas of active research. This volume is aimed at researchers in discrete and convex geometry and researchers who work with abstract polytopes or string $C$-groups. It is also aimed at early career mathematicians, including graduate students and postdoctoral fellows, to give them a glimpse of the variety and beauty of these research areas. Topics covered in this volume include: the combinatorics, geometry, and symmetries of convex polytopes; tilings; discrete point sets; the combinatorics of Eulerian posets and interval posets; symmetries of surfaces and maps on surfaces; self-dual polytopes; string $C$-groups; hypertopes; and graph coloring.

Spis treści

• M. M. Bayer, The $cd$-index: A survey
• T. Bisztriczky and D. Oliveros, $d$-dimensional self-dual polytopes and Meissner polytopes
• P. A. Brooksbank, On the ranks of string $C$-group representations for symplectic and orthogonal groups
• J. Damasco and D. Frettloh, Perfect colorings of regular graphs
• J. A. De Loera, T. A. Hogan, F. Meunier, and N. H. Mustafa, Tverberg theorems over discrete sets of points
• A. Deza, L. Pournin, and R. Rakotonarivo, The vertices of primitive zonotopes
• M. G. Dobbins and F. Frick, Barycenters of points in polytope skeleta
• M. E. Fernandes, D. Leemans, C. Piedade, and A. I. Weiss, Two families of locally toroidal regular 4-hypertopes arising from toroids
• A. Jensen, Self-polar polytopes
• K.-i. Kawarabayashi, P. Klavik, B. Mohar, R. Nedela, and P. Zeman, Isomorphisms of maps on the sphere
• J. Lawrence, Some enumeration relating to intervals in posets
• D. Leemans, String $C$-group representations of almost simple groups: A survey
• U. Leopold and T. W. Tucker, Orientation-reversing symmetry of closed surfaces immersed in Euclidean 3-space
• P. McMullen, Realizations of the 120-cell
• E. Schulte, P. Soberon, and G. I. Williams, Prescribing symmetries and automorphisms for polytopes
• M. Senechal and J. E. Taylor, The rhombic triacontahedron and crystallography
• M. D. Tomenes and M. L. A. N. De Las Penas, Tilings with congruent edge coronae.