53 citations · 186 across the 27 of their papers we have counts for
4 papers · 1 filter
A combinatorial formula for the nabla operator
Erik Carlsson, Anton Mellit
We present an LLT-type formula for a general power of the nabla operator applied to the Cauchy product for the modified Macdonald polynomials, and use it to deduce a new proof of t…
A proof of the compositional Delta conjecture
Michele D'Adderio, Anton Mellit
We prove a compositional refinement of the Delta conjecture (rise version) of Haglund, Remmel and Wilson (2018) for which was stated by D'Adderio, Iraci and Van…
Toric braids and -parking functions
Anton Mellit
The Dyck path algebra construction of Carlsson and Mellit from arXiv:1508.06239 is interpreted as a representation of "the positive part" of the group of toric braids. Then certain…
Five-term relation and Macdonald polynomials
Adriano Garsia, Anton Mellit
The non-commutative five-term relation is shown to hold for certain operators acting on symmetric functions. The "generalized recursion"…