The principal minors of a matroid
نویسندگان
چکیده
منابع مشابه
Minors of a Random Binary Matroid
Let A = An,m,k be a random n × m matrix over GF2 where each column consists of k randomly chosen ones. Let M be an arbirary fixed binary matroid. We show that if m/n and k are sufficiently large then as n → ∞ the binary matroid induced by A contains M as a minor.
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The algebraic relations between the principal minors of an n× n matrix are somewhat mysterious, see e.g. [LS09]. We show, however, that by adding in certain almost principal minors, the relations are generated by a single relation, the so-called hexahedron relation, which is a composition of six cluster mutations. We give in particular a Laurent-polynomial parameterization of the space of n× n ...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1971
ISSN: 0024-3795
DOI: 10.1016/0024-3795(71)90026-7