2020/05/01 by Tristram Bogart, Bogart, Tristram, João Pedro Gouveia +3
Business, Management and Accounting · Engineering · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Mathematics and Applications #Product Development and Customization #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2005.00640
openalex publication_date 2020/05/01 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
A combinatorial polytope P is said to be projectively unique if it has a\nsingle realization up to projective transformations. Projective uniqueness is a\ngeometrically compelling property but is difficult to verify. In this paper, we\nmerge two approaches to projective uniqueness in the literature. One is\nprimarily geometric and is due to McMullen, who showed that certain natural\noperations on polytopes preserve projective uniqueness. The other is more\nalgebraic and is due to Gouveia, Macchia, Thomas, and Wiebe. They use certain\nideals associated to a polytope to verify a property called graphicality that\nimplies projective uniqueness. In this paper, we show that that McMullen's\noperations preserve not only projective uniquness but also graphicality. As an\napplication, we show that large families of order polytopes are graphic and\nthus projectively unique.\n