On the automorphism conjecture for products of ordered sets |
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Authors: | N. N. Kuzjurin |
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Affiliation: | (1) Institute of Cybernetics, Russian Academy of Science, Vavilova, 37, 117312 Moscow, Russia |
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Abstract: | I. Rival and A. Rutkowski conjectured that the ratio of the number of automorphisms of an arbitrary poset to the number of order-preserving maps tends to zero as the size of the poset tends to infinity. We prove this hypothesis for direct products of arbitrary posets P=S1××Sn under the condition that maxi|Si|=0(n/logn). |
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Keywords: | Primary: 05A15 06A17 |
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