The fixed point property for finite posets of width 3 and 4 is studied in
terms of forbidden retracts. The ranked forbidden retracts for width 3 and 4
are determined explicitly. The ranked forbidden retracts for the width 3 case
that are linearly indecomposable are examined to see which are minimal
automorphic. Part of a problem of Niederle from 1989 is thus solved

Farley, Jonathan David

English

arXiv

. The fixed point property for finite posets of width 3 and 4 is studied in terms of forbidden retracts. The ranked forbidden retracts for width 3 and 4 are determined explicitly. The ranked forbidden retracts for the width 3 case that are linearly indecomposable are examined to see which are minimal automorphic. Part of a problem of Niederle from 1989 is thus solved. 1. Introduction.  How does one recognize a poset with the fixed point property? The problem has a long history ([12]). Recently, it was shown to be computationally intractable ([4], Theorem 1.1). Nonetheless, for certain classes of ordered sets, the posets with the fixed point property have been characterized, generally in terms of forbidden retracts: A finite, connected rank 1 poset has the fixed point property if and only if no crown is a retract. (There is also a characterization for the infinite rank 1 posets in terms of forbidden suborders. See [11], Theorem; [10], T heorem 4.) A finite, N-free poset of dimension 2 h..

Jonathan David Farley

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The Fixed Point Property For Posets Of Small Width

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The Fixed Point Property for Posets of Small Width

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