Patchworks

Böcker S, Dress A (2001)
Advances in Mathematics 157(1): 1-21.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Böcker, Sebastian; Dress, AndreasUniBi
Abstract / Bemerkung
In this note, we want to introduce a concept that as we shall see-exhibits all interesting relationship with hierarchies: We define a collection T subset of or equal to P(X) of subsets of a set X to be a patchwork if empty set not equal C subset of or equal to C and boolean AND (C is an element ofC) C not equal empty set implies boolean AND (C is an element ofC) C is an element of C and boolean OR (C is an element ofC) C is an element of C. In this note. we will investigate patchworks C that contain a maximal hierarchy. We will show this holds if and only if (i) the empty subset empty set. all one-element subsets {x} (x is an element of X) of X, and the set X itself belong to C. and (ii) the patchwork is ample, that is, A, B is an element of C and #{C is an element of C / A subset of or equal to C subset of or equal to B} = 2 implies B - A is an element of C. (C) Academic Press.
Stichworte
maximal hierarchies; the category of cluster systems; ample cluster systems; hierarchical clustering; finitary cluster systems; hierarchies; patchworks; cluster systems; lattices
Erscheinungsjahr
2001
Zeitschriftentitel
Advances in Mathematics
Band
157
Ausgabe
1
Seite(n)
1-21
ISSN
0001-8708
Page URI
https://pub.uni-bielefeld.de/record/1618048

Zitieren

Böcker S, Dress A. Patchworks. Advances in Mathematics. 2001;157(1):1-21.
Böcker, S., & Dress, A. (2001). Patchworks. Advances in Mathematics, 157(1), 1-21. https://doi.org/10.1006/aima.1999.1912
Böcker, S., and Dress, A. (2001). Patchworks. Advances in Mathematics 157, 1-21.
Böcker, S., & Dress, A., 2001. Patchworks. Advances in Mathematics, 157(1), p 1-21.
S. Böcker and A. Dress, “Patchworks”, Advances in Mathematics, vol. 157, 2001, pp. 1-21.
Böcker, S., Dress, A.: Patchworks. Advances in Mathematics. 157, 1-21 (2001).
Böcker, Sebastian, and Dress, Andreas. “Patchworks”. Advances in Mathematics 157.1 (2001): 1-21.

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