Zobrazeno 1 - 10
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pro vyhledávání: '"Polak, Sven"'
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 region defined by polynomial (in)equalities. A key feature of the hiera
Externí odkaz:
http://arxiv.org/abs/2305.14944
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 $A\subseteq V_1$, $B\subseteq V_2$ and $A\cup B$ is independent. These parameters also allow to study bi
Externí odkaz:
http://arxiv.org/abs/2302.08886
Autor:
Brosch, Daniel1,2 (AUTHOR), C. Polak, Sven2,3 (AUTHOR) s.c.polak@tilburguniversity.edu
Publikováno v:
Mathematical Programming. Sep2024, Vol. 207 Issue 1/2, p693-715. 23p.
Autor:
Brosch, Daniel, Polak, Sven
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 method from de Klerk et al. [SIAM J. Discrete Math. 20 (2006), 189--202
Externí odkaz:
http://arxiv.org/abs/2206.02755
Publikováno v:
Examples and Counterexamples, 2 (2022), 100051
A code $\mathcal{C} \subseteq \{0, 1, 2\}^n$ is said to be trifferent with length $n$ when for any three distinct elements of $\mathcal{C}$ there exists a coordinate in which they all differ. Defining $\mathcal{T}(n)$ as the maximum cardinality of tr
Externí odkaz:
http://arxiv.org/abs/2201.06846
Autor:
Gribling, Sander, Polak, Sven
Publikováno v:
Quantum 8, 1318 (2024)
A set of $k$ orthonormal bases of $\mathbb C^d$ is called mutually unbiased if $|\langle e,f\rangle |^2 = 1/d$ whenever $e$ and $f$ are basis vectors in distinct bases. A natural question is for which pairs $(d,k)$ there exist~$k$ mutually unbiased b
Externí odkaz:
http://arxiv.org/abs/2111.05698
Autor:
Polak, Sven
Publikováno v:
SIAM Journal on Applied Algebra and Geometry, 6 (2022), 243-266
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 $n$ vertices and coefficients depending on cardinalities of certain unio
Externí odkaz:
http://arxiv.org/abs/2104.08264
Autor:
Polak, Sven
In this thesis we present several results in coding theory, concerning error-correcting codes and the Shannon capacity. 1. We give a general symmetry reduction of matrices occuring in semidefinite programs in coding theory. 2. We apply the symmetry r
Externí odkaz:
http://arxiv.org/abs/2005.02945
Autor:
Polak, Sven
Publikováno v:
Discrete Mathematics, 342 (2019), 2579-2589
For $q,n,d \in \mathbb{N}$, let $A_q^L(n,d)$ denote the maximum cardinality of a code $C \subseteq \mathbb{Z}_q^n$ with minimum Lee distance at least $d$, where $\mathbb{Z}_q$ denotes the cyclic group of order $q$. We consider a semidefinite programm
Externí odkaz:
http://arxiv.org/abs/1810.05066
Autor:
Polak, Sven, Schrijver, Alexander
Publikováno v:
Information Processing Letters, 143 (2019), 37-40
We give an independent set of size $367$ in the fifth strong product power of $C_7$, where $C_7$ is the cycle on $7$ vertices. This leads to an improved lower bound on the Shannon capacity of $C_7$: $\Theta(C_7)\geq 367^{1/5} > 3.2578$. The independe
Externí odkaz:
http://arxiv.org/abs/1808.07438