A. Pun

activity

20162021

collaborators

Showing math.COShow all

6 papers · 1 filter

math.CO2021

A proof of the Extended Delta Conjecture

Jonah Blasiak, Mark Haiman, Jennifer Morse +2

We prove the Extended Delta Conjecture of Haglund, Remmel, and Wilson, a combinatorial formula for $Δ_{h_{l}} Δ_{e_{k}}^{'} e_{n}$ , where $Δ_{e_{k}}^{'}$ and $Δ_{h_{l}}$ are Macdonald eigenoper…

math.CO2021

A Shuffle Theorem for Paths Under Any Line

Jonah Blasiak, Mark Haiman, Jennifer Morse +2

We generalize the shuffle theorem and its $(k m, k n)$ version, as conjectured by Haglund et al. and Bergeron et al., and proven by Carlsson and Mellit, and Mellit, respectively. In o…

math.CO2020

Demazure crystals and the Schur positivity of Catalan functions

Jonah Blasiak, Jennifer Morse, Anna Pun

Catalan functions, the graded Euler characteristics of certain vector bundles on the flag variety, are a rich class of symmetric functions which include $k$ -Schur functions and par…

math.CO2018

$k$ -Schur expansions of Catalan functions

Jonah Blasiak, Jennifer Morse, Anna Pun +1

We make a broad conjecture about the $k$ -Schur positivity of Catalan functions, symmetric functions which generalize the (parabolic) Hall-Littlewood polynomials. We resolve the con…

math.CO2018

Catalan functions and $k$ -Schur positivity

Jonah Blasiak, Jennifer Morse, Anna Pun +1

We prove that graded $k$ -Schur functions are $G$ -equivariant Euler characteristics of vector bundles on the flag variety, settling a conjecture of Chen-Haiman. We expose a new mira…

math.CO2016

On Deposition of the Product of Demazure Atoms and Demazure Characters

Anna Ying Pun

This paper studies the properties of Demazure atoms and characters using linear operators and also tableaux-combinatorics. It proves the atom-positivity property of the product of…