Vertex Operators for Standard Bases of the Symmetric Functions
Mike Zabrocki
DOI: 10.1023/A:1008732003019
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.
Pages: 83–101
Keywords: symmetric functions; vertex operators
Full Text: PDF
References
1. F. Bergeron, L. Favreau, and D. Krob, “Conjectures on the enumeration of tableaux of bounded height,” Discrete Mathematics 139 (1995), 463-468.
2. N. Jing, “Vertex operators and Hall-Littlewood symmetric functions,” Adv. Math. 87 (1991), 226-248.
3. I.G. Macdonald, Symmetric Functions and Hall Polynomials, Oxford Mathematical Monographs, Oxford UP, 2nd ed., 1995.
4. M.A. Zabrocki, “A Macdonald vertex operator and standard tableaux statistics for the two-column (q, t)-Kostka coefficients,” Electron. J. Combinat. 5 (R45) (1998), 46.
5. A.V. Zelevinsky, Representations of Finite Classical Groups: A Hopf Algebra Approach, Springer Lecture Notes, 869, 1981.
2. N. Jing, “Vertex operators and Hall-Littlewood symmetric functions,” Adv. Math. 87 (1991), 226-248.
3. I.G. Macdonald, Symmetric Functions and Hall Polynomials, Oxford Mathematical Monographs, Oxford UP, 2nd ed., 1995.
4. M.A. Zabrocki, “A Macdonald vertex operator and standard tableaux statistics for the two-column (q, t)-Kostka coefficients,” Electron. J. Combinat. 5 (R45) (1998), 46.
5. A.V. Zelevinsky, Representations of Finite Classical Groups: A Hopf Algebra Approach, Springer Lecture Notes, 869, 1981.