Vertex Operators for Standard Bases of the Symmetric Functions |
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Authors: | Mike Zabrocki |
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Affiliation: | (1) CRM, Univeristé de Montréal, LaCIM, Université du Québec à Montréal, C.P. 8888, Succ. A, Montréal, Canada, H3C 3P8 |
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Abstract: | We present formulas for operators which add a row or a column to the partition indexing the power, monomial, forgotten, Schur, homogeneous and elementary symmetric functions. As an application of these operators we show that the operator that adds a column to the Schur unctions can be used to calculate a formula for the number of pairs of standard tableaux the same shape and height less than or equal to a fixed k. |
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Keywords: | symmetric functions vertex operators |
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