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    Electronic Resource
    Electronic Resource
    Automorphisms and isotone self-maps of ordered sets with top and bottom (1993)
    Springer
    Order 10 (1993), S. 105-110 
    Details
    ISSN: 1572-9273
    Keywords: 06A07 ; 06A12 ; 05E25 ; 20B25 ; Automorphism ; isotone self-map ; irreducible element
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For an ordered setP letP P denote the set of all isotone self-maps on P, that is, all mapsf fromP toP such thatx≥y impliesf(x)≥f(y), and let Aut (P) the set of all automorphisms onP, that is, all bijective isotone self-maps inP P . We establish an inequality relating ¦P P ¦ and ¦Aut(P)¦ in terms of the irreducibles ofP. As a straightforward corollary, we show that Rival and Rutkowski's automorphism conjecture is true for lattices. It is also true for ordered sets with top and bottom whose covering graphs are planar.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01111294
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