Pseudo-similar points in ordered sets

Pseudo-similar points in ordered sets

Two points l and h in an ordered set P are called pseudo-similar iff P ∖ { l } is isomorphic to P ∖ { h } and there is no automorphism of P that maps l to h . This paper provides a characterization of ordered sets with at least two pseudo-similar points. Special attention is given to ordered sets wi...

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Veröffentlicht in:Discrete mathematics 2010-11, Vol.310 (21), p.2815-2823
1. Verfasser: Schroeder, Bernd SW
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Automorphisms
Cards
Combinatorics
Combinatorics. Ordered structures
Exact sciences and technology
Isomorphic cards
Mathematical analysis
Mathematics
Maximal card
Minimal card
Order, lattices, ordered algebraic structures
Ordered set
Pseudo-similar points
Reconstruction
Sciences and techniques of general use
Set reconstruction
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Beschreibung
Zusammenfassung:Two points l and h in an ordered set P are called pseudo-similar iff P ∖ { l } is isomorphic to P ∖ { h } and there is no automorphism of P that maps l to h . This paper provides a characterization of ordered sets with at least two pseudo-similar points. Special attention is given to ordered sets with pseudo-similar points l and h so that one of the points is minimal and the other is maximal. These sets will play a key role in the reconstruction of the rank of the removed element in a non-extremal card.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2010.06.022