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Bihomogeneous symmetric functions

Part of: Algebraic combinatorics Spectral theory and eigenvalue problems

Published online by Cambridge University Press:  25 May 2021

Yuly Billig
Yuly Billig*
Affiliation:
School of Mathematics and Statistics, Carleton University, Ottawa, ON, Canada
*
e-mail: [email protected]
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Abstract

We consider two natural gradings on the space of symmetric functions: by degree and by length. We introduce a differential operator T that leaves the components of this double grading invariant and exhibit a basis of bihomogeneous symmetric functions in which this operator is triangular. This allows us to compute the eigenvalues of T, which turn out to be nonnegative integers.

Keywords

Symmetric functions

MSC classification

Primary: 05E05: Symmetric functions and generalizations
Secondary: 35P05: General topics in linear spectral theory
Type
Article
Information
Canadian Mathematical Bulletin , Volume 65 , Issue 2 , June 2022 , pp. 400 - 408
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Copyright
© Canadian Mathematical Society 2021

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Footnotes

Support from the Natural Sciences and Engineering Research Council of Canada is gratefully acknowledged.

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