Vertex operators for standard bases of the symmetric functions

Details Vertex operators for standard bases of the symmetric functions Vertex operators for standard bases of the symmetric functions

1999-04-16

arxiv.org/abs/math/9904084v1

Mathematics

Combinatorics

22 pages. Material presented at seminar talk 'How to grow symmetric functions.' Maple programs for formulas available at htt

Scientific paper

We present a formulas to add a row or a column to 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 functions 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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