Some Quotients of Chain Products are Symmetric Chain Orders
نویسندگان
چکیده
منابع مشابه
Some Quotients of Chain Products are Symmetric Chain Orders
Canfield and Mason have conjectured that for all subgroups G of the automorphism group of the Boolean lattice Bn (which can be regarded as the symmetric group Sn) the quotient order Bn/G is a symmetric chain order. We provide a straightforward proof of a generalization of a result of K. K. Jordan: namely, Bn/G is an SCO whenever G is generated by powers of disjoint cycles. In addition, the Bool...
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Subgroups of the symmetric group Sn act on C n (the n-fold product C×· · ·×C of a chain C) by permuting coordinates, and induce automorphisms of the power Cn. For certain families of subgroups of Sn, the quotients defined by these groups can be shown to have symmetric chain decompositions (SCDs). These SCDs allow us to enlarge the collection of subgroups G of Sn for which the quotient 2 n/G on ...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2012
ISSN: 1077-8926
DOI: 10.37236/2430