The Automorphism Conjecture for Ordered Sets of Dimension 2 and Interval Orders

The Automorphism Conjecture for Ordered Sets of Dimension 2 and Interval Orders

Let λ ∈ 0 , 1 2 . We prove that, for ordered sets P of order dimension 2 and for interval orders, the ratio of the number of automorphisms to the number of endomorphisms is asymptotically bounded by 2 − | P | λ . The key to the proof is to establish this bound for certain types of lexicographic sums...

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Veröffentlicht in:Order (Dordrecht) 2021-07, Vol.38 (2), p.271-281
1. Verfasser: Schröder, Bernd S. W.
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Automorphisms
Discrete Mathematics
Lattices
Mathematics
Mathematics and Statistics
Order
Ordered Algebraic Structures
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Zusammenfassung:Let λ ∈ 0 , 1 2 . We prove that, for ordered sets P of order dimension 2 and for interval orders, the ratio of the number of automorphisms to the number of endomorphisms is asymptotically bounded by 2 − | P | λ . The key to the proof is to establish this bound for certain types of lexicographic sums.
ISSN:0167-8094
1572-9273
DOI:10.1007/s11083-020-09540-5