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

Dress A, Terhalle W (1995)
Applied Mathematics Letters 8(4): 19-23.

Zeitschriftenaufsatz | Veröffentlicht | Englisch

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Autor*in
Dress, AndreasUniBi; Terhalle, Werner
Abstract / Bemerkung
Given a finite set E and a map f : P(E) --> R boolean OR {-infinity}, we define f to be well-layered, if and only if for every map eta : E --> R and every finite sequency e(1), e(2), ..., e(i) is an element of E with # {e(1), ..., e(i)} = i and f({e(1), ..., e(j)}) + Sigma(k=1)(j) eta(e(k)) greater than or equal to f({e(1), ..., e(j-1),e}) + Sigma(k=1)(j-1) eta(e(k)) + eta(e) for all j = 1, ..., i and e is an element of E/{e(1), ..., e(j-1)}, one has f({e(1), ..., e(i)}) + Sigma(k=1)(i) eta(e(k)) greater than or equal to f (I) + Sigma(e is an element of I) eta(e) for every I subset of or equal to E with # (J/I) greater than or equal to 3 and with f(I) not equal -infinity or I = 0 and for every a is an element of J/I, there exists some b is an element of J/(I boolean OR {a}) with f (I boolean OR {a}) + f (J/{a}) less than or equal to f (I boolean OR {b}) + f (J/{b}) = -infinity 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 releated to control theory.
Stichworte
VALUATED MATROIDS; MATROIDS; VALUATED DELTA-MATROIDS; GREEDY; ALGORITHMS; GREEDOIDS
Erscheinungsjahr
1995
Zeitschriftentitel
Applied Mathematics Letters
Band
8
Ausgabe
4
Seite(n)
19-23
ISSN
0893-9659
Page URI
https://pub.uni-bielefeld.de/record/1640509

### Zitieren

Dress A, Terhalle W. Well-layered maps and the maximum-degree k × k-subdeterminant of a matrix of rational functions. Applied Mathematics Letters. 1995;8(4):19-23.
Dress, A., & Terhalle, W. (1995). Well-layered maps and the maximum-degree k × k-subdeterminant of a matrix of rational functions. Applied Mathematics Letters, 8(4), 19-23. https://doi.org/10.1016/0893-9659(95)00040-W
Dress, A., and Terhalle, W. (1995). Well-layered maps and the maximum-degree k × k-subdeterminant of a matrix of rational functions. Applied Mathematics Letters 8, 19-23.
Dress, A., & Terhalle, W., 1995. Well-layered maps and the maximum-degree k × k-subdeterminant of a matrix of rational functions. Applied Mathematics Letters, 8(4), p 19-23.
A. Dress and W. Terhalle, “Well-layered maps and the maximum-degree k × k-subdeterminant of a matrix of rational functions”, Applied Mathematics Letters, vol. 8, 1995, pp. 19-23.
Dress, A., Terhalle, W.: Well-layered maps and the maximum-degree k × k-subdeterminant of a matrix of rational functions. Applied Mathematics Letters. 8, 19-23 (1995).
Dress, Andreas, and Terhalle, Werner. “Well-layered maps and the maximum-degree k × k-subdeterminant of a matrix of rational functions”. Applied Mathematics Letters 8.4 (1995): 19-23.

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