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Improved cap constructions, and sets without arithmetic progressions
Virtualconference
Authors : Elsholtz, Christian (Author of the conference)
CIRM (Publisher )
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 (Publisher )
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Abstract :
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
MSC Codes : 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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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 01/12/2020 Conference Date : 24/11/2020 Subseries : Research talks arXiv category : Combinatorics ; Number Theory Mathematical Area(s) : Number Theory ; Combinatorics ; Geometry Format : MP4 (.mp4) - HD Video Time : 00:52:53 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2020-11-24_Elshotz.mp4 
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Information on the Event
Event Title : Jean-Morlet Chair 2020 - Conference: Diophantine Problems, Determinism and Randomness / Chaire Jean-Morlet 2020 - Conférence : Problèmes diophantiens, déterminisme et aléatoireEvent Organizers : Rivat, Joël ; Tichy, Robert Dates : 23/11/2020 - 27/11/2020 Event Year : 2020 Event URL : https://www.chairejeanmorlet.com/2256.html
Citation Data
DOI : 10.24350/CIRM.V.19692603Cite this video as: 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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