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Titolo:
ON THE INTERPLAY BETWEEN INTERVAL DIMENSION AND DIMENSION
Autore:
FELSNER S; HABIB M; MOHRING RH;
Indirizzi:
TECH UNIV BERLIN BERLIN GERMANY LAB INFORMAT ROBOT MICROELECTR MONTPELLIER MONTPELLIER FRANCE
Titolo Testata:
SIAM journal on discrete mathematics
fascicolo: 1, volume: 7, anno: 1994,
pagine: 32 - 40
SICI:
0895-4801(1994)7:1<32:OTIBID>2.0.ZU;2-M
Fonte:
ISI
Lingua:
ENG
Soggetto:
GRAPHS; COMPARABILITY; FAMILIES;
Keywords:
PARTIAL ORDER; DIMENSION; INTERVAL DIMENSION; INTERVAL ORDER; GEOMETRIC REPRESENTATION OF ORDERED SETS;
Tipo documento:
Article
Natura:
Periodico
Settore Disciplinare:
CompuMath Citation Index
Science Citation Index Expanded
Citazioni:
23
Recensione:
Indirizzi per estratti:
Citazione:
S. Felsner et al., "ON THE INTERPLAY BETWEEN INTERVAL DIMENSION AND DIMENSION", SIAM journal on discrete mathematics, 7(1), 1994, pp. 32-40

Abstract

This paper investigates a transformation P->Q between partial orders P, Q that transforms the interval dimension of P to the dimension of Q, i.e., idim (P) = dim (Q). Such a construction has been shown before in the context of Ferrer's dimension by Cogis [Discrete Math., 38 (1982), pp. 47-52]. The construction in this paper can be shown to be equivalent to his, but it has the advantage oft I) being purely order-theoretic, (2) providing a geometric interpretation of interval dimension similar to that of Ore [Amer. Math. Soc. Colloq. Publ., Vol. 38, 1962]for dimension, and (3) revealing several somewhat surprising connections to other order-theoretic results. For instance, the transformationP->Q and can be seen as almost an inverse of the well-known split operation; it provides a theoretical background for the influence of edgesubdivision on dimension (e.g., the results of Spinrad [Order, 5 (1989), pp. 143-147]) and interval dimension, and it turns out to be invariant with respect to changes of P that do not alter its comparability graph, thus also providing a simple new proof for the comparability invariance of interval dimension.

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Documento generato il 29/03/20 alle ore 11:45:21