Hong Chen

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6 papers · 1 filter

math.CO2026

Correlation inequalities for Schur positivity

Swee Hong Chan, Hong Chen, Igor Pak +1

We generalize the Ahlswede--Daykin inequality (1978) to a Schur positive \emph{ADS inequality}, which also contains the Lam--Postnikov--Pylyavskyy inequality (2007) as a special ca…

math.CO2026

A Characterization of the Macdonald Hypergeometric Series $_{r} Φ_{s} (x; q, t)$ and $_{r} Φ_{s} (x, y; q, t)$ via $q$ -Difference Equations

Hong Chen

In two widely circulated manuscripts from the 1980s, I. G. Macdonald introduced certain multivariate hypergeometric series $_{p} F_{q} (x; α)$ and $_{p} F_{q} (x, y; α)$ and their $q$ -analogs…

math.CO2025

A Characterization of Macdonald's Jack Hypergeometric Series $_{p} F_{q} (x; α)$ and $_{p} F_{q} (x, y; α)$ 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 $_{p} F_{q} (x) =_{p} F_{q} (x; α)$ and…

math.CO2025

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…

math.CO2025

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…

math.CO2024

Interpolation Polynomials, Binomial Coefficients, and Symmetric Function Inequalities

Hong Chen, Siddhartha Sahi

Interpolation polynomials were introduced by Knop--Sahi in type $A$ , and Okounkov in type $B C$ . They are inhomogeneous polynomials whose top terms are Jack and Macdonald polynomial…

Correlation inequalities for Schur positivity

A Characterization of the Macdonald Hypergeometric Series r​Φs​(x;q,t) and r​Φs​(x,y;q,t) via q-Difference Equations

A Characterization of Macdonald's Jack Hypergeometric Series p​Fq​(x;α) and p​Fq​(x,y;α) via Differential Equations

Majorization via positivity of Jack and Macdonald polynomial differences

Monotonicity for generalized binomial coefficients and Jack positivity

Interpolation Polynomials, Binomial Coefficients, and Symmetric Function Inequalities

A Characterization of the Macdonald Hypergeometric Series $_{r} Φ_{s} (x; q, t)$ and $_{r} Φ_{s} (x, y; q, t)$ via $q$ -Difference Equations

A Characterization of Macdonald's Jack Hypergeometric Series $_{p} F_{q} (x; α)$ and $_{p} F_{q} (x, y; α)$ via Differential Equations