Vertex operators for standard bases of the symmetric functions
Abstract
Description
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 $k$.
22 pages. Material presented at seminar talk 'How to grow symmetric functions.' Maple programs for formulas available at http://www.lacim.uqam.ca/~zabrocki/maple/Vertex.html
22 pages. Material presented at seminar talk 'How to grow symmetric functions.' Maple programs for formulas available at http://www.lacim.uqam.ca/~zabrocki/maple/Vertex.html