Sven Polak

activity

20162023

most citedSpin-orbit Interactions for Singlet-Triplet Qubits in Silicon

64 citations · 127 across the 14 of their papers we have counts for

collaborators

15 papers

math.OC2023

A note on the computational complexity of the moment-SOS hierarchy for polynomial optimization

Sander Gribling, Sven Polak, Lucas Slot

The moment-sum-of-squares (moment-SOS) hierarchy is one of the most celebrated and widely applied methods for approximating the minimum of an n-variate polynomial over a feasible r…

math.CO2023

Semidefinite approximations for bicliques and biindependent pairs

Monique Laurent, Sven Polak, Luis Felipe Vargas

We investigate some graph parameters dealing with biindependent pairs $(A, B)$ in a bipartite graph $G = (V_{1} \cup V_{2}, E)$ , i.e., pairs $(A, B)$ where $A \subseteq V_{1}$ , $B \subseteq V_{2}$ …

math.CO2022★ 1 cited

New lower bounds on crossing numbers of $K_{m, n}$ from semidefinite programming

Daniel Brosch, Sven Polak

In this paper, we use semidefinite programming and representation theory to compute new lower bounds on the crossing number of the complete bipartite graph $K_{m, n}$ , extending a m…

math.CO2022★ 7 cited

The maximum cardinality of trifferent codes with lengths 5 and 6

Stefano Della Fiore, Alessandro Gnutti, Sven Polak

A code $C \subseteq {0, 1, 2}^{n}$ is said to be trifferent with length $n$ when for any three distinct elements of $C$ there exists a coordinate in which they…

math.OC2021

Mutually unbiased bases: polynomial optimization and symmetry

Sander Gribling, Sven Polak

A set of $k$ orthonormal bases of $C^{d}$ is called mutually unbiased if $∣ ⟨ e, f ⟩ ∣^{2} = 1/ d$ whenever $e$ and $f$ are basis vectors in distinct bases. A natural q…

math.CO2021★ 4 cited

Symmetry reduction to optimize a graph-based polynomial from queueing theory

Sven Polak

For given integers $n$ and $d$ , both at least 2, we consider a homogeneous multivariate polynomial $f_{d}$ of degree $d$ in variables indexed by the edges of the complete graph on $n…

math.CO2018★ 6 cited

Semidefinite programming bounds for Lee codes

Sven Polak

For $q, n, d \in N$ , let $A_{q}^{L} (n, d)$ denote the maximum cardinality of a code $C \subseteq Z_{q}^{n}$ with minimum Lee distance at least $d$ , where $Z_{q}$ deno…

cond-mat.mes-hall2018★ 64 cited

Spin-orbit Interactions for Singlet-Triplet Qubits in Silicon

Patrick Harvey-Collard, N. Tobias Jacobson, Chloé Bureau-Oxton +12

Spin-orbit coupling is relatively weak for electrons in bulk silicon, but enhanced interactions are reported in nanostructures such as the quantum dots used for spin qubits. These…

math.CO2018★ 3 cited

On the circular chromatic number of a subgraph of the Kneser graph

Bart Litjens, Sven Polak, Bart Sevenster +1

Let $n, k, r$ be positive integers with $n \geq r k$ and $r \geq 2$ . Consider a circle $C$ with~ $n$ points~ $1, \dots, n$ in clockwise order. The $r$ -stable \emph{interlacing graph} $\t…

math.CO2017★ 2 cited

Sum-perfect graphs

Bart Litjens, Sven Polak, Vaidy Sivaraman

Inspired by a famous characterization of perfect graphs due to Lovász, we define a graph $G$ to be sum-perfect if for every induced subgraph $H$ of $G$ , $α (H) + ω (H) \geq ∣ V (H) ∣$ .…

math.CO2017

Uniqueness of codes using semidefinite programming

Andries E. Brouwer, Sven C. Polak

For $n, d, w \in N$ , let $A (n, d, w)$ denote the maximum size of a binary code of word length $n$ , minimum distance $d$ and constant weight $w$ . Schrijver recently showed usin…

math.CO2017★ 13 cited

Semidefinite programming bounds for constant weight codes

Sven Polak

For nonnegative integers $n, d, w$ , let $A (n, d, w)$ be the maximum size of a code $C \subseteq F_{2}^{n}$ with constant weight $w$ and minimum distance at least $d$ . We consider…

math.CO2016

Improved upper bound on A(18,8)

Sven Polak

For nonnegative integers $n$ and $d$ , let $A (n, d)$ be the maximum cardinality of a binary code of length $n$ and minimum distance at least $d$ . We consider a slight sharpening of t…

math.CO2016★ 1 cited

New nonbinary code bounds based on divisibility arguments

Sven Polak

For $q, n, d \in N$ , let $A_{q} (n, d)$ be the maximum size of a code $C \subseteq [q]^{n}$ with minimum distance at least $d$ . We give a divisibility argument resulting in the ne…

math.CO2016★ 26 cited

Semidefinite bounds for nonbinary codes based on quadruples

Bart Litjens, Sven Polak, Alexander Schrijver

For nonnegative integers $q, n, d$ , let $A_{q} (n, d)$ denote the maximum cardinality of a code of length $n$ over an alphabet $[q]$ with $q$ letters and with minimum distance at least $…

A note on the computational complexity of the moment-SOS hierarchy for polynomial optimization

Semidefinite approximations for bicliques and biindependent pairs

New lower bounds on crossing numbers of Km,n​ from semidefinite programming

The maximum cardinality of trifferent codes with lengths 5 and 6

Mutually unbiased bases: polynomial optimization and symmetry

Symmetry reduction to optimize a graph-based polynomial from queueing theory

Semidefinite programming bounds for Lee codes

Spin-orbit Interactions for Singlet-Triplet Qubits in Silicon

On the circular chromatic number of a subgraph of the Kneser graph

Sum-perfect graphs

Uniqueness of codes using semidefinite programming

Semidefinite programming bounds for constant weight codes

Improved upper bound on A(18,8)

New nonbinary code bounds based on divisibility arguments

Semidefinite bounds for nonbinary codes based on quadruples

New lower bounds on crossing numbers of $K_{m, n}$ from semidefinite programming