Symmetric Chain Decompositions of Quotients of Chain Products by Wreath Products
Duffus, Dwight · Thayer, Kyle
Original · EN
Subgroups of the symmetric group Sₙ act on powers of chains Cⁿ by permuting coordinates, and induce automorphisms of the ordered sets Cⁿ. The quotients defined are candidates for symmetric chain decompositions. We establish this for some families of groups in order to enlarge the collection of subgroups G of the symmetric group Sₙ for which the quotient Bₙ/G obtained from the G-orbits on the Boolean lattice Bₙ is a symmetric chain order. The methods are also used to provide an elementary proof that quotients of powers of SCOs by cyclic groups are SCOs.
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