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      On the basis of the burnside ring of a fusion system

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      Author
      Gelvin, M.
      Reeh, S.P.
      Yalçın, E.
      Date
      2015
      Source Title
      Journal of Algebra
      Print ISSN
      0021-8693
      Electronic ISSN
      1090-266X
      Publisher
      Elsevier
      Volume
      423
      Pages
      767 - 797
      Language
      English
      Type
      Article
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      Abstract
      We consider the Burnside ring A(F) of F-stable S-sets for a saturated fusion system F defined on a p-group S. It is shown by S.P. Reeh that the monoid of F-stable sets is a free commutative monoid with canonical basis {αP}. We give an explicit formula that describes αP as an S-set. In the formula we use a combinatorial concept called broken chains which we introduce to understand inverses of modified Möbius functions. © 2014 Elsevier Inc.
      Keywords
      Burnside ring
      Fusion systems
      Mobius function
      Permalink
      http://hdl.handle.net/11693/22569
      Published Version (Please cite this version)
      http://dx.doi.org/10.1016/j.jalgebra.2014.10.026
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