Open AccessLargest induced suborders satisfying the chain condition
Author(s) -
Nathan Linial,
Michael Saks,
Peter W. Shor
Publication year - 1985
Publication title -
order
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.465
H-Index - 27
eISSN - 1572-9273
pISSN - 0167-8094
DOI - 10.1007/bf00333132
Subject(s) - cardinality (data modeling) , mathematics , combinatorics , chain (unit) , dedekind cut , discrete mathematics , astronomy , computer science , data mining , physics
For a finite ordered set P, let c(P) denote the cardinality of the largest subset Q such that the induced suborder on Q satisfies the Jordan-Dedekind chain condition (JDCC), i.e., every maximal chain in Q has the same cardinality. For positive integers n, let f(n) be the minimum of c(P) over all ordered sets P of cardinality n. We prove: $$\sqrt {2n } - 1 \leqslant f (n) \leqslant 4 e \sqrt {n.}$$
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