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Majorization Inequalities from Logarithmic Convexity
Colin McSwiggen, Siddhartha Sahi
Majorization inequalities for symmetric polynomials have interested mathematicians for centuries, from the AM-GM inequality for two variables going back at least to BaudhÄyana's Å…
Interpolation Polynomials, Binomial Coefficients, and Symmetric Function Inequalities
Hong Chen, Siddhartha Sahi
Interpolation polynomials were introduced by Knop--Sahi in type , and Okounkov in type . They are inhomogeneous polynomials whose top terms are Jack and Macdonald polynomial…
Majorization via positivity of Jack and Macdonald polynomial differences
Hong Chen, Apoorva Khare, Siddhartha Sahi
Majorization inequalities have a long history, going back to Maclaurin and Newton. They were recently studied for several families of symmetric functions, including by Cuttler--Gre…
A Characterization of Macdonald's Jack Hypergeometric Series and via Differential Equations
Hong Chen, Siddhartha Sahi
In a widely circulated manuscript from the 1980s, now available on the arXiv, I.~G.~Macdonald introduced certain multivariable hypergeometric series and…
Monotonicity for generalized binomial coefficients and Jack positivity
Hong Chen, Siddhartha Sahi
Binomial formulas for Schur polynomials and Jack polynomials were studied by Lascoux in 1978, and Kaneko, Okounkov--Olshanski and Lassalle in the 1990s. We prove that the associate…