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The lattice automorphisms of the dominance ordering

✍ Scribed by Rodica Simion

Publisher
Elsevier Science
Year
1984
Tongue
English
Weight
180 KB
Volume
49
Category
Article
ISSN
0012-365X

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✦ Synopsis

In this paper it is shown that the lattice/_~ of partitions of n under the dominance ordering is totally asymmetric, except for the cases n = 6 and 7 where the automorphism group is Z2XZ 2. As a consequence, partition conjugation is the only antiautomorphism of/_~ if n ~ 6, 7.

L 6 and L 7 the automorphism group is isomorphic to 7/2 x 7/2, while for all other n, /_~ is totally asymmetric, i.e., Aut(/_~)= {1}.

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