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Counting with Nonstandard Bases

  • Anthony Mendes
  • Jeffrey Remmel
Chapter
  • 1.1k Downloads
Part of the Developments in Mathematics book series (DEVM, volume 43)

Abstract

Generalizing the relationship between the elementary and power symmetric functions, we define a new basis for the ring of symmetric functions which has an expansion in terms of specially weighted brick tabloids. This allows us even more versatility when using symmetric functions in enumerating permutations and words. We show how this new basis can be used to find generating functions for various refinements of permutations and words, recurrence relations, and objects counted by the exponential formula.

Keywords

Power Symmetric Functions Exponential Formula Alternative Permutations Defined Ring Homomorphism Final Brick 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Anthony Mendes
    • 1
  • Jeffrey Remmel
    • 2
  1. 1.Mathematics DepartmentCalifornia Polytechnic State UniversitySan Luis ObispoUSA
  2. 2.Department of MathematicsUniversity of California at San DiegoLa JollaUSA

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