Abstract
The Jack symmetric function J λ( x;α) is a symmetric function with interesting properties that J λ( x;2) is a spherical function of the symmetric pair ( GL( n, R ), O( n, R ) and that J λ ( x;1) is the Schur function S λ( x). Many interesting conjectures about the combinatorial properties of J λ( x;α) are given by Stanley (1989). In this paper we give an affirmative answer to one of his conjectures.
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