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On sumsets and convex hull

Author
Boeroeczky, K.; Santos, F.; Serra, O.
Type of activity
Journal article
Journal
Discrete and computational geometry
Date of publication
2014-12-01
Volume
52
Number
4
First page
705
Last page
729
DOI
https://doi.org/10.1007/s00454-014-9633-2 Open in new window
Project funding
Optimización y problemas extremales en teoria de grafos y combinatoria. Aplicacions a les redes de comunicación
URL
http://link.springer.com/article/10.1007%2Fs00454-014-9633-2 Open in new window
Abstract
One classical result of Freiman gives the optimal lower bound for the cardinality of if is a -dimensional finite set in . Matolcsi and Ruzsa have recently generalized this lower bound to if is -dimensional, and is contained in the convex hull of . We characterize the equality case of the Matolcsi-Ruzsa bound. The argument is based partially on understanding triangulations of polytopes.
Keywords
Shellable triangulations, Sumsets, h-vector
Group of research
GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics

Participants

  • Boeroeczky, Karoly J  (author)
  • Santos Leal, Francisco  (author)
  • Serra Albo, Oriol  (author)