Journal Article

Symmetric Chain Decomposition for Cyclic Quotients of Boolean Algebras and Relation to Cyclic Crystals

Patricia Hersh and Anne Schilling

in International Mathematics Research Notices

Volume 2013, issue 2, pages 463-473
Published in print January 2013 | ISSN: 1073-7928
Published online January 2012 | e-ISSN: 1687-0247 | DOI: https://dx.doi.org/10.1093/imrn/rnr254

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The quotient of a Boolean algebra by a cyclic group is proved to have a symmetric chain decomposition. This generalizes earlier work of Griggs, Killian and Savage on the case of prime order, giving an explicit construction for any order, prime or composite. The combinatorial map specifying how to proceed downward in a symmetric chain is shown to be a natural cyclic analog of the lowering operator in the theory of crystal bases.

Journal Article.  3439 words.  Illustrated.

Subjects: Mathematics