Geodesic
Some quotients of chain products are symmetric chain orders
Dwight Duffus1 ; Jeremy McKibben-Sanders2 ; Kyle Thayer2
1Math & CS Department, Emory University
2Emory University
The electronic journal of combinatorics, Tome 19 (2012) no. 2
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Canfield and Mason have conjectured that for all subgroups $G$ of the automorphism group of the Boolean lattice $B_n$ (which can be regarded as the symmetric group $S_n$), the quotient order $B_n/G$ is a symmetric chain order. We provide a straightforward proof of a generalization of a result of K. K. Jordan: namely, $B_n/G$ is an SCO whenever $G$ is generated by powers of disjoint cycles. In addition, the Boolean lattice $B_n$ can be replaced by any product of finite chains. The symmetric chain decompositions of Greene and Kleitman provide the basis for partitions of these quotients.
DOI : 10.37236/2430
Classification : 06A07, 20B25
Mots-clés : symmetric chain decomposition, Boolean lattice, quotients

Dwight Duffus  1   ; Jeremy McKibben-Sanders  2   ; Kyle Thayer  2

1 Math & CS Department, Emory University
2 Emory University 
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Dwight Duffus; Jeremy McKibben-Sanders; Kyle Thayer. Some quotients of chain products are symmetric chain orders. The electronic journal of combinatorics, Tome 19 (2012) no. 2. doi: 10.37236/2430

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