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This article is cited in 4 scientific papers (total in 4 papers)
Virtual polytopes
G. Yu. Paninaab, I. Streinuc a St. Petersburg State University
b St. Petersburg Institute for Informatics and Automation of the Russian Academy of Sciences
c Department of Computer Science, Smith College, Northampton, MA, USA
Abstract:
Originating in diverse branches of mathematics, from polytope algebra and toric varieties to the theory of stressed graphs, virtual polytopes represent a natural algebraic generalization of convex polytopes. Introduced as elements of the Grothendieck group associated to the semigroup of convex polytopes, they admit a variety of geometrizations. The present survey connects the theory of virtual polytopes with other geometrical subjects, describes a series of geometrizations together with relations between them, and gives a selection of applications.
Bibliography: 50 titles.
Keywords:
Minkowski difference, coloured polygon, polytopal function, support functions, stressed graph, McMullen's polytope algebra, Maxwell polytope.
Received: 10.12.2014 Revised: 04.10.2015
Citation:
G. Yu. Panina, I. Streinu, “Virtual polytopes”, Uspekhi Mat. Nauk, 70:6(426) (2015), 139–202; Russian Math. Surveys, 70:6 (2015), 1105–1165
Linking options:
https://www.mathnet.ru/eng/rm9639https://doi.org/10.1070/RM2015v070n06ABEH004975 https://www.mathnet.ru/eng/rm/v70/i6/p139
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Abstract page: | 893 | Russian version PDF: | 560 | English version PDF: | 42 | References: | 86 | First page: | 64 |
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