Let (A, R) be a poset in which the length of a longest (maximal) chain is n

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Let (A, R) be a poset in which the length of a longest (maximal) chain is n ≥ 2. Let M be the set of all maximal elements in (A, R), and let B = A - M. If R' = (B × B) ⋂ R, prove that the length of a longest chain in (B, R') is n - 1.

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Discrete and Combinatorial Mathematics An Applied Introduction

ISBN: 978-0201726343

5th edition

Authors: Ralph P. Grimaldi

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Question Posted: Jun 21, 2016 08:34 AM

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Let (A, R) be a poset in which the length of a longest (maximal) chain is n

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Let a 1 Ra 2 RRa n1 Ra n be a longest maximal chain in A R Then a n is a m...View the full answer

Discrete and Combinatorial Mathematics An Applied Introduction

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