BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Sandor Kiss (Budapest University of Technology and Economics) DTSTART:20250520T153000Z DTEND:20250520T155500Z DTSTAMP:20260423T010356Z UID:CANT2025/17 DESCRIPTION:Title: Generalized Stanley sequences\nby Sandor Kiss (Budapest University o f Technology and Economics) as part of Combinatorial and additive number t heory (CANT 2025)\n\nLecture held in CUNY Graduate Center - Science Center (4th floor).\n\nAbstract\nFor an integer $k \\ge 3$\, let $A_{0} = \\{a_ {1}\, \\dots{} \,a_{t}\\}$ be a set of nonnegative integers which does not contain an arithmetic progression of length $k$. The set $S(A)$ is define d by the following greedy algorithm. If $s \\ge t$ and $a_{1}\, \\dots{} \ ,a_{s}$ have already been defined\, then\n$a_{s+1}$ is the smallest intege r $a > a_{s}$ such that $\\{a_{1}\, \\dots{} \,a_{s}\\} \\cup \\{a\\}$ als o does not contain a $k$-term arithmetic progression. The sequence $S(A)$ is called a \n\\emph{Stanley sequence} of order $k$ generated by $A_{0}$. Starting out from a set of the form $A_{0} = \\{0\, t\\}$\, Richard P. Sta nley and Odlyzko tried to generate arithmetic progression-free sets by usi ng the greedy algorithm. In 1999\, Erd\\H{o}s\, Lev\, Rauzy\, S\\'andor an d S\\'ark\\"ozy extended the notion of Stanley sequence to other initial s ets $A_{0}$. In my talk I investigate some further generalizations of Stan ley sequences and I give some density type results about them. \nThis is a joint work with Csaba S\\'andor and Quan-Hui Yang.\n LOCATION:https://researchseminars.org/talk/CANT2025/17/ END:VEVENT END:VCALENDAR