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SUMMARY:Carlo Sanna (Politecnico di Torino\, Italy)
DTSTART:20220526T133000Z
DTEND:20220526T135500Z
DTSTAMP:20260423T011320Z
UID:CANT2022/32
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/32/
 ">Membership in random ratio sets</a>\nby Carlo Sanna (Politecnico di Tori
 no\, Italy) as part of Combinatorial and additive number theory (CANT 2022
 )\n\n\nAbstract\nLet $\\mathcal{A}$ be a random set constructed by picking
  independently each element of $\\{1\, \\dots\, n\\}$ with probability $\\
 alpha \\in (0\, 1)$.\nSeveral authors studied combinatorial/number-theoret
 ic objects involving $\\mathcal{A}$\, including the sum set $\\mathcal{A} 
 + \\mathcal{A}$\, the product set $\\mathcal{A}\\mathcal{A}$\, and the rat
 io set $\\mathcal{A} /\\! \\mathcal{A}$.\nGeneralizing a previous result o
 f Cilleruelo and Guijarro-Ord\\'{o}\\~{n}ez\, we give a formula for the pr
 obability that a rational number $q$ belongs to the ratio set $\\mathcal{A
 } /\\! \\mathcal{A}$.\nMoreover\, we give some results about formulas for 
 the probability of the event $\\bigvee_{i=1}^k\\!\\big(q_i \\in \\mathcal{
 A} /\\! \\mathcal{A}\\big)$\, where $q_1\, \\dots\, q_k$ are rational numb
 ers\, showing that they are related to the study of the connected componen
 ts of certain graphs.\nFinally\, we provide some open question for future 
 research.\n
LOCATION:https://researchseminars.org/talk/CANT2022/32/
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