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Further counterexamples to the monotonicity property of t-step maintainable structures

Published online by Cambridge University Press:  14 July 2016

John Haigh*
Affiliation:
University of Sussex
*
Postal address: Mathematics Division, University of Sussex, Falmer, Brighton BN1 9QH, UK.

Abstract

Until Guerry's (1990) counterexample to a conjecture of Davies about three-state hierarchical organisations kept at constant size via annual promotion, wastage and recruitment, it was easy to believe that such structures maintainable in t steps would also be maintainable in t + 1 steps. Here we present further counterexamples, which show that t-step maintainability does not imply (t + 1)-step maintainability, for astonishingly large values of t.

Type
Short Communications
Copyright
Copyright © Applied Probability Trust 1992 

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