Some combinatorial properties of Jack symmetric functions
Tài liệu tham khảo
Constantine, 1963, Some noncentral distribution problems in multivariate analysis, Ann. Math. Statist., 34, 1270, 10.1214/aoms/1177703863
P. Diaconis and E. Lander, Some formulas for zonal polynomials, in preparation.
Foulkes, 1974, A survey of some combinatorial aspects of symmetric functions
Hanlon, 1988, Jack symmetric functions and some combinatorial properties of Young symmetrizers, J. Combin. Theory Ser. A, 47, 37, 10.1016/0097-3165(88)90042-8
Jack, 1969, A class of symmetric polynomials with a parameter, 69, 1
James, 1961, Zonal polynomials of the real positive definite symmetric matrices, Ann. of Math., 74, 456, 10.2307/1970291
James, 1964, Distributions of matrix variables and latent roots derived from normal samples, Ann. Math. Statist., 35, 475, 10.1214/aoms/1177703550
James, 1968, Calculation of zonal polynomial coefficients by use of the Laplace-Beltrami operator, Ann. Math. Statist., 39, 1711, 10.1214/aoms/1177698153
H. B. Kushner, The linearization of the product of two zonal polynomials, preprint.
Kerber, 1983, Symmetrieklassen von Funktionen und ihre Abzählungstheorie, Bayreuther Mathematische Schriften
Littlewood, 1950
Macdonald, 1979
Macdonald, 1987, Commuting differential equations and zonal spherical functions, Vol. 1271, 189
[M3]I. G. Macdonald, [M1], 2nd ed., to appear.
Specht, 1960, Die Characktere der symmetrichen Gruppe, Math. Zeit., 73, 312, 10.1007/BF01215313
Takemura, 1984, Zonal Polynomials, Vol. 4