English
Improved cap constructions, and sets without arithmetic progressions
Virtualconference
Auteurs : Elsholtz, Christian (Auteur de la Conférence)
CIRM (Editeur )
05B25 - Finite geometries, See also {51D20, 51Exx}
51E20 - Combinatorial structures in finite projective spaces, See also {05Bxx}
51E22 - Linear codes and caps in Galois spaces, See also {94B05}
CIRM (Editeur )
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Résumé :
A cap is a point set in affine or projective space without any three points on any line. We will discuss the current state of
the art, and give an exponential improvement for the size of caps of AG(n, p), which one can think of as (Z/pZ)^n, and PG(n,p). For certain primes, 5,11,17,23,29 and 41, we improve the asymptotic growth of these caps, for example, when p=23 from (8.091...)^n to (9-o(1))^n, as n tends to infinity.
Keywords : caps; sets without arithmetic progressions in affine or projective space
Codes MSC : the art, and give an exponential improvement for the size of caps of AG(n, p), which one can think of as (Z/pZ)^n, and PG(n,p). For certain primes, 5,11,17,23,29 and 41, we improve the asymptotic growth of these caps, for example, when p=23 from (8.091...)^n to (9-o(1))^n, as n tends to infinity.
Keywords : caps; sets without arithmetic progressions in affine or projective space
05B25 - Finite geometries, See also {51D20, 51Exx}
51E20 - Combinatorial structures in finite projective spaces, See also {05Bxx}
51E22 - Linear codes and caps in Galois spaces, See also {94B05}
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 01/12/2020 Date de captation : 24/11/2020 Sous collection : Research talks arXiv category : Combinatorics ; Number Theory Domaine : Number Theory ; Combinatorics ; Geometry Format : MP4 (.mp4) - HD Durée : 00:52:53 Audience : Researchers Download : https://videos.cirm-math.fr/2020-11-24_Elshotz.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Jean-Morlet Chair 2020 - Conference: Diophantine Problems, Determinism and Randomness / Chaire Jean-Morlet 2020 - Conférence : Problèmes diophantiens, déterminisme et aléatoireOrganisateurs de la rencontre : Rivat, Joël ; Tichy, Robert Dates : 23/11/2020 - 27/11/2020 Année de la rencontre : 2020 URL Congrès : https://www.chairejeanmorlet.com/2256.html
Données de citation
DOI : 10.24350/CIRM.V.19692603Citer cette vidéo: Elsholtz, Christian (2020). Improved cap constructions, and sets without arithmetic progressions. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19692603 URI : http://dx.doi.org/10.24350/CIRM.V.19692603 |
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