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Description
  • (Tento článek je konferenční abstrakt) Definuje se, že dvě bodové množiny A,B v rovině mají stejnou projekci ve směru u, pokud každá přímka rovnoběžná s u obsahuje stejný bočet bodů z A jako bodů z B. Definuje se F(k) jako největší n takové, že existuje k-tice směrů, pro něž žádné dvě n=bodové množiny nemají stejné projekce ve všech těchto k směrech zároveň. Dokazují se dolní a horní odhady pro F(k), které jsou poměrně blízké. Používá se kombinace lineárně-algebraických, kombinatorických a pravděpodobnostních metod. (cs)
  • (This paper is an extended abstract.) We say that two point sets A,B have identical X-rays in direction u if every line parallel to u contains the same number of points of A as points of B. We define F(k) as the maximum n such that there exist k directions for which no two n-point sets have the same X-rays in all of these k directions. We give almost matching upper and lower bounds on F(k) by a combination of linear-algebraic, combinatorial, and probabilistic methods.
  • (This paper is an extended abstract.) We say that two point sets A,B have identical X-rays in direction u if every line parallel to u contains the same number of points of A as points of B. We define F(k) as the maximum n such that there exist k directions for which no two n-point sets have the same X-rays in all of these k directions. We give almost matching upper and lower bounds on F(k) by a combination of linear-algebraic, combinatorial, and probabilistic methods. (en)
Title
  • How many points can be reconstructed from k projections?
  • How many points can be reconstructed from k projections? (en)
  • Kolik bodů lze rekonstruovat z k projekcí? (cs)
skos:prefLabel
  • How many points can be reconstructed from k projections?
  • How many points can be reconstructed from k projections? (en)
  • Kolik bodů lze rekonstruovat z k projekcí? (cs)
skos:notation
  • RIV/00216208:11320/07:00005004!RIV08-MSM-11320___
http://linked.open.../vavai/riv/strany
  • 427;434
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(1M0545), P(GD201/05/H014), Z(MSM0021620838)
http://linked.open...iv/cisloPeriodika
  • C
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 424824
http://linked.open...ai/riv/idVysledku
  • RIV/00216208:11320/07:00005004
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • points; reconstructed; projections (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • NL - Nizozemsko
http://linked.open...ontrolniKodProRIV
  • [611EBB549C06]
http://linked.open...i/riv/nazevZdroje
  • Electronic Notes in Discrete Mathematics
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 29
http://linked.open...iv/tvurceVysledku
  • Matoušek, Jiří
  • Přívětivý, Aleš
  • Škovroň, Petr
http://linked.open...n/vavai/riv/zamer
issn
  • 1571-0653
number of pages
http://localhost/t...ganizacniJednotka
  • 11320
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