Symmetric functions in noncommuting variables |
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| Authors: | Mercedes H. Rosas Bruce E. Sagan |
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| Affiliation: | Departamento de Matemáticas, Universidad Simón Bolívar, Apdo. Postal 89000, Caracas, Venezuela ; Department of Mathematics, Michigan State University, East Lansing, Michigan 48824-1027 |
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| Abstract: | Consider the algebra  of formal power series in countably many noncommuting variables over the rationals. The subalgebra  of symmetric functions in noncommuting variables consists of all elements invariant under permutation of the variables and of bounded degree. We develop a theory of such functions analogous to the ordinary theory of symmetric functions. In particular, we define analogs of the monomial, power sum, elementary, complete homogeneous, and Schur symmetric functions as well as investigating their properties. |
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| Keywords: | Noncommuting variables partition lattice Schur function symmetric function |
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