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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 Baudhāyana's Śu…
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…
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…
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…
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…
Interpolation polynomials, bar monomials, and their positivity
Yusra Naqvi, Siddhartha Sahi, Emily Sergel
We prove a positivity result for interpolation polynomials that was conjectured by Knop and Sahi. These polynomials were first introduced by Sahi in the context of the Capelli eige…