Download or read book A Product Formula for Certain Littlewood-Richardson Coefficients for Jack and Macdonald Polynomials written by Yusra Fatima Naqvi and published by . This book was released on 2014 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt: Jack polynomials generalize several classical families of symmetric polynomials, including Schur polynomials, and are further generalized by Macdonald polynomials. In 1989, Richard Stanley conjectured that if the Littlewood-Richardson coefficient for a triple of Schur polynomials is 1, then the corresponding coefficient for Jack polynomials can be expressed as a product of weighted hooks of the Young diagrams associated to the partitions indexing the coefficient. We prove a special case of this conjecture in which the partitions indexing the Littlewood-Richardson coefficient have at most 3 parts. We also show that this result extends to Macdonald polynomials.