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Dens, nests and the Loehr-Warrington conjecture
Jonah Blasiak, Mark Haiman, Jennifer Morse +2
In a companion paper, we introduced raising operator series called Catalanimals. Among them are Schur Catalanimals, which represent Schur functions inside copies $Λ(X^{m,n})\subset…
LLT polynomials in the Schiffmann algebra
Jonah Blasiak, Mark Haiman, Jennifer Morse +2
We identify certain combinatorially defined rational functions which, under the shuffle to Schiffmann algebra isomorphism, map to LLT polynomials in any of the distinguished copies…
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…