Daniel Orr

activity

20242026

collaborators

4 papers

math.CO2026

Combinatorial proof of a permuted basement Macdonald polynomial identity

Daniel Orr, Johnny Rivera

A well-known and fundamental property of the Macdonald polynomials $P_{I^} » (x; q, t)$ is their invariance under the transformation sending $(q, t)$ to $(q^{- 1}, t^{- 1})$ . Recently, Concha…

math.AG2025

Toda-Type Presentations for the Quantum K Theory of Partial Flag Varieties

Kamyar Amini, Irit Huq-Kuruvilla, Leonardo C. Mihalcea +2

We prove a determinantal, Toda-type, presentation for the equivariant K theory of a partial flag variety $Fl (r_{1}, \dots, r_{k}; n)$ . The proof relies on pushing forward the Toda…

math.CO2024

Stable-limit partially symmetric Macdonald functions and parabolic flag Hilbert schemes

Daniel Orr, Milo Bechtloff Weising

The modified Macdonald functions $H_{I^} ¼$ are fundamental objects in modern algebraic combinatorics. Haiman showed that there is a correspondence between the $(\mathbb{C}…

math.CO2024

A Geometric Realization of Partially-Symmetric Macdonald Polynomials

Ben Goodberry, Daniel Orr

We formulate a precise conjecture relating integral form partially-symmetric Macdonald polynomials and the parabolic flag Hilbert schemes of Carlsson, Gorsky, and Mellit. This exte…