6 papers · 1 filter
The nonsymmetric shuffle theorem
Jonah Blasiak, Mark Haiman, Jennifer Morse +2
The shuffle conjecture of Haglund et al. expresses the symmetric function as a sum over labeled Dyck paths. Here is an operator on symmetric functions defined…
Flagged LLT polynomials, nonsymmetric plethysm, and nonsymmetric Macdonald polynomials
Jonah Blasiak, Mark Haiman, Jennifer Morse +2
The plethystic transformation and LLT polynomials are central to the theory of symmetric Macdonald polynomials. In this work, we introduce and study nonsy…
A raising operator formula for Macdonald polynomials
Jonah Blasiak, Mark Haiman, Jennifer Morse +2
We give an explicit raising operator formula for the modified Macdonald polynomials , which follows from our recent formula for on an LLT polynomial…
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 , where and are Macdonald eigenoper…
A Shuffle Theorem for Paths Under Any Line
Jonah Blasiak, Mark Haiman, Jennifer Morse +2
We generalize the shuffle theorem and its version, as conjectured by Haglund et al. and Bergeron et al., and proven by Carlsson and Mellit, and Mellit, respectively. In o…
-theoretic Catalan functions
Jonah Blasiak, Jennifer Morse, George H. Seelinger
We prove that the --Schur functions are part of a family of inhomogenous symmetric functions whose top homogeneous components are Catalan functions, the Euler characteristics…