Well-layered maps and the maximum-degree k × k-subdeterminant of a matrix of rational functions

✍ Scribed by A.W.M. Dress; W. Terhalle

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 297 KB
• Volume: 8
• Category: Article
• ISSN: 0893-9659
• DOI: 10.1016/0893-9659(95)00040-w

✦ Synopsis

for every I _C E with #I = i. In this note, we show that a map f is well-layered if and only if for every I C J C E with #(J\I) ~ 3 and with f(I) • -oo or I = 0 and for every a E J\I, there exists some b E J(I U {a}) with f(I U {a}) -F f(g{a}) <_ f(I U {b}) + f(Z{b}), and if in addition f(I) = -oo for all subsets I of some fixed cardinality i with 0 < i < #E implies f(I') = -oo for all subsets I' with i < #I' < #E. In addition, we provide some "generic" examples of well-layered maps related to p-adic geometry, and we indicate some interesting applications related to control theory.