Realizable but not Strongly Euclidean Oriented Matroids^†

Author: Santos F.

Source: European Journal of Combinatorics, Volume 22, Number 5, July 2001 , pp. 767-776(10)

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Abstract:

The extension space conjecture of oriented matroid theory claims that the space of all (non-zero, non-trivial, single-element) extensions of a realizable oriented matroid of rank r is homotopy equivalent to an (r - 1)-sphere. In 1993, Sturmfels and Ziegler proved the conjecture for the class of strongly Euclidean oriented matroids, which includes those of rank at most 3 or corank at most 2. They did not provide any example of a realizable but not strongly Euclidean oriented matroid. Here we produce two such examples for the first time, one with rank 4 and one with corank 3. Both have 12 elements. Copyright 2001 Academic Press

Language: English

Document Type: Research article

Affiliations: Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria, Santander, E-39005, Spain

Publication date: 2001-07-01