10 citations · 26 across the 8 of their papers we have counts for
8 papers
Anchored Dyck Paths
Jimmy Dillies
We answer a question of Simental by providing a combinatorial interpretation of a formula which generalizes rational Catalan numbers and which appears in the study of Springer fibe…
On Suffridge polynomials
Jimmy Dillies, Dmitriy Dmitrishin, Alex Stokolos
We consider some known and some new properties of the family of polynomials introduced by Ted Suffridge in 1969. We begin by giving a brief overview of their extremal properties in…
On the Koebe Quarter Theorem for Polynomials
Jimmy Dillies, Dmitriy Dmitrishin, Andrey Smorodin +1
D. Dimitrov has posed the problem of finding polynomials that set the sharpness of the Koebe Quarter Theorem for polynomials and asked whether Suffridge polynomials are optimal. We…
Univalence of a certain quartic function
Jimmy Dillies
We give a short proof that the quartic polynomial is univalent.
The Inverse Problem of Quartic Photonics
Thomas Mulkey, Jimmy Dillies, Maxim Durach
We propose an approach to engineer quartic metamaterials starting from the desired photonic states. We apply our method to the design of the high-k asymptotics of metamaterials, ex…
Example of an order 16 non symplectic action on a K3 surface
Jimmy Dillies
We exhibit an example of a K3 surface of Picard rank with a non-symplectic automorphism of order which fixes a rational curve and isolated points. This settles the e…
Generalized Borcea-Voisin Construction
Jimmy Dillies
C. Voisin and C. Borcea have constructed mirror pairs of families of Calabi-Yau threefolds by taking the quotient of the product of an elliptic curve with a K3 surface endowed with…
Order 6 non-symplectic automorphisms of K3 surfaces
Jimmy Dillies
We classify primitive non-symplectic automorphisms of order 6 on K3 surfaces. We show how their study can be reduced to the study of non-symplectic automorphisms of order 3 and to…