Regular Article: Sparse Interpolation of Symmetric Polynomials

Authors:
Alexander Barvinok;Sergey Fomin
Affiliations:
Department of Mathematics, University of Michigan, Ann Arbor, Michigan, 48109-1003;Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts, 02139 and Theory of Algorithms Laboratory, St. Petersburg Institute of Informatics, Russian Academy of S ...
Venue:
Advances in Applied Mathematics
Year:
1997

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On the complexity of computing Kostka numbers and Littlewood-Richardson coefficients

Journal of Algebraic Combinatorics: An International Journal

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Abstract

We develop efficient algorithms for computing the expansion of a given symmetric polynomial into Schur functions. This problem frequently arises in applications as the problem of decomposing a given representation of the symmetric (or general linear) group into irreducible constituents. Our algorithms are probabilistic, and run in time which is polynomial in the sizes of the input and output. They can be used to compute Littlewood-Richardson coefficients, Kostka numbers, and irreducible characters of the symmetric group.