9 citations · 10 across the 8 of their papers we have counts for
5 papers · 1 filter
A Proof the Functional Equation Conjecture
Adriano Garsia, Angela Hicks, Guoce Xin
In the early 2000's the first and second named authors worked for a period of six years in an attempt of proving the Compositional Shuffle Conjecture [1]. Their approach was based…
A simpler formula for the number of diagonal inversions of an (m,n)-Parking Function and a returning Fermionic formula
Angela Hicks, Emily Leven
Recent results have placed the classical shuffle conjecture of Haglund et al. in a broader context of an infinite family of conjectures about parking functions in any rectangular l…
A refinement of the Shuffle Conjecture with cars of two sizes and
Angela Hicks, Emily Leven
The original Shuffle Conjecture of Haglund et al. has a symmetric function side and a combinatorial side. The symmetric function side may be simply expressed as …
Statistics on parallelogram polyominoes and a q,t-analogue of the Narayana numbers
Jean-Christophe Aval, Michele D'Adderio, Mark Dukes +2
We study the statistics area, bounce and dinv on the set of parallelogram polyominoes having a rectangular m times n bounding box. We show that the bi-statistics (area, bounce) and…
A Parking Function Bijection supporting the Haglund-Morse-Zabrocki Conjectures
Angela Hicks
The shuffle conjecture expresses a relationship between parking functions, diagonal harmonics, and the Bergeron-Garsia operator. Recent conjectures about a family of modif…