New lower bound on the Shannon capacity of C7 from circular graphs

Autor: Alexander Schrijver, Sven Polak

Publikováno v: Information Processing Letters, 143, 37-40
Information Processing Letters, 143, 37-40. Elsevier

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: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fa2ce816586ec7b2462c3c4e5e8a6e20
https://doi.org/10.1016/j.ipl.2018.11.006

Semidefinite bounds for nonbinary codes based on quadruples

Autor: Alexander Schrijver, Bart Litjens, Sven Polak

Publikováno v: Designs, Codes, and Cryptography
Designs, Codes and Cryptography, 84, 87-100
Designs, Codes and Cryptography, 84(1-2), 87-100. Springer Netherlands

For nonnegative integers q, n, d, let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt}

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::528c247773c52e7f1adba4bec872622a
https://doi.org/10.1007/s10623-016-0216-5

Characterizing partition functions of the edge-coloring model by rank growth

Autor: Alexander Schrijver

Publikováno v: Journal of Combinatorial Theory. Series A, 136, 164-173. Academic Press Inc.
Journal of Combinatorial Theory-Series A, 136, 164-173

We characterize which graph invariants are partition functions of an edge-coloring model over the complex numbers, in terms of the rank growth of associated `connection matrices'.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a9543cc979aeca476a71639b38bc77cb
https://doi.org/10.1016/j.jcta.2015.06.007

Analysis of multi-stage open shop processing systems

Autor: Christian E. J. Eggermont, Alexander Schrijver, Gerhard J. Woeginger

Publikováno v: Mathematical programming, 142(1-2), 331-348. Springer-Verlag GmbH and Co. KG
Mathematical Programming, 142(1-2), 331-348. Springer
Mathematical Programming, 142, 331-348

We study algorithmic problems in multi-stage open shop processing systems that are centered around reachability and deadlock detection questions. We characterize safe and unsafe system states. We show that it is easy to recognize system states that c

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ca318b73c366883c9a17c08125115410
https://dare.uva.nl/personal/pure/en/publications/analysis-of-multistage-open-shop-processing-systems(c8bd456f-ef3d-47cd-9086-4699e3c2a407).html

Characterizing partition functions of the vertex model

Autor: Guus Regts, Jan Draisma, László Lovász, Dion Gijswijt, Alexander Schrijver

Publikováno v: Journal of Algebra, 350(1), 197-206. Academic Press Inc.
Journal of Algebra, 350(1), 197-206

We characterize which graph parameters are partition functions of a vertex model over an algebraically closed field of characteristic 0 (in the sense of [P. de la Harpe, V.F.R. Jones, Graph invariants related to statistical mechanical models: example

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7e934e43bc03b5cc5a45cd9666c298a1
https://dare.uva.nl/personal/pure/en/publications/characterizing-partition-functions-of-the-vertex-model(7bbc989b-1d88-4d50-bf0a-afca901b7a75).html