BEGIN:VCALENDAR VERSION:2.0 PRODID:-//wp-events-plugin.com//7.2.3.1//EN TZID:Europe/Paris X-WR-TIMEZONE:Europe/Paris BEGIN:VEVENT UID:8534@i2m.univ-amu.fr DTSTART;TZID=Europe/Paris:20250429T110000 DTEND;TZID=Europe/Paris:20250429T120000 DTSTAMP:20250430T083728Z URL:https://www.i2m.univ-amu.fr/evenements/tba-200/ SUMMARY:Matthieu Rosenfeld (LIRMM\, Montpellier): Local obstructions in seq uences revisited DESCRIPTION:Matthieu Rosenfeld: Consider the following problem about lacuna ry sequences of positive integers\, i.e.\, nₖ₊₁>\;(1+e)nₖ for so me e>\;0: Can we find a real θ such that the distances from nₖθ to t he nearest integer are bounded away from 0?\n\nNow consider a second probl em: Given some c<\;2\, does there exist a constant N and an infinite bin ary sequence α such that for every string x of length n≥N\, any two occ urrences of x in α are far away\, i.e.\, the distance between them is at least ~cⁿ?\n\nFor both questions\, one can use the Lovasz Local Lemma (L LL) to prove the existence of the desired objects. However\, this is not c onstructive\, in the sense that one cannot deduce from the LLL the existen ce of a computable θ or α.\n\nIn this talk\, after giving some context\, I will present a seemingly unrelated simple combinatorial game and a simp le winning strategy in this game. I will then use this game to prove compu table versions of these results (also slightly improving the previous boun ds).\n\nThese results are based on a recent preprint with Alexander Shen. CATEGORIES:Séminaire,Ernest LOCATION:I2M Luminy - TPR2\, Salle de Séminaire 304-306 (3ème étage)\, 1 63 Avenue de Luminy\, Marseille\, 13009\, France X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=163 Avenue de Luminy\, Mars eille\, 13009\, France;X-APPLE-RADIUS=100;X-TITLE=I2M Luminy - TPR2\, Sall e de Séminaire 304-306 (3ème étage):geo:0,0 END:VEVENT BEGIN:VTIMEZONE TZID:Europe/Paris X-LIC-LOCATION:Europe/Paris BEGIN:DAYLIGHT DTSTART:20250330T030000 TZOFFSETFROM:+0100 TZOFFSETTO:+0200 TZNAME:CEST END:DAYLIGHT END:VTIMEZONE END:VCALENDAR