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.
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Mendes, A., Remmel, J. (2015). Counting with Nonstandard Bases. In: Counting with Symmetric Functions. Developments in Mathematics, vol 43. Springer, Cham. https://doi.org/10.1007/978-3-319-23618-6_4
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DOI: https://doi.org/10.1007/978-3-319-23618-6_4
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