Subgroup Lattices and Symmetric Functions

Released on by Lynne M. Butler
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  • Subgroup Lattices and Symmetric Functions Book Detail

  • Author : Lynne M. Butler
  • Release Date : 1994
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 173
  • ISBN 13 : 082182600X
  • File Size : 83,83 MB
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Subgroup Lattices and Symmetric Functions by Lynne M. Butler PDF Summary

Book Description: This work presents foundational research on two approaches to studying subgroup lattices of finite abelian p-groups. The first approach is linear algebraic in nature and generalizes Knuth's study of subspace lattices. This approach yields a combinatorial interpretation of the Betti polynomials of these Cohen-Macaulay posets. The second approach, which employs Hall-Littlewood symmetric functions, exploits properties of Kostka polynomials to obtain enumerative results such as rank-unimodality. Butler completes Lascoux and Schützenberger's proof that Kostka polynomials are nonnegative, then discusses their monotonicity result and a conjecture on Macdonald's two-variable Kostka functions.

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