Abstract
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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Communicated by D. Duffus
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Linial, N., Saks, M. & Shor, P. Largest induced suborders satisfying the chain condition. Order 2, 265–268 (1985). https://doi.org/10.1007/BF00333132
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DOI: https://doi.org/10.1007/BF00333132