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The Mixed Volumes and Geissinger Multiplications of Convex Sets
Author(s) -
Chen Beifang
Publication year - 1994
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm199491139
Subject(s) - mixed volume , mathematics , multiplication (music) , regular polygon , minkowski space , volume (thermodynamics) , representation (politics) , minkowski addition , identity (music) , polynomial , convex body , pure mathematics , mathematical analysis , combinatorics , convex optimization , geometry , physics , quantum mechanics , politics , political science , acoustics , law
This paper introduces Geissinger multiplication on the vector space generated by indicator functions of closed convex sets. Minkowski's mixed volume for compact convex sets is naturally represented in terms of the volume of the Geissinger multiplication of their indicator functions. Some properties of mixed volumes and new results are obtained by this representation, including a polynomial identity.