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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 is their invariance under the transformation sending to . Recently, Concha…
math.CO2024
Stable-limit partially symmetric Macdonald functions and parabolic flag Hilbert schemes
Daniel Orr, Milo Bechtloff Weising
The modified Macdonald functions 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…