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PRODID:researchseminars.org
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X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Mel Nathanson (CUNY)
DTSTART:20260910T190000Z
DTEND:20260910T200000Z
DTSTAMP:20260906T220842Z
UID:NYNTS/1
DESCRIPTION:Title: <a href="https://master.researchseminars.org/talk/NYNTS
 /1/">Sidon sets with Delta-separated sumsets</a>\nby Mel Nathanson (CUNY) 
 as part of New York Number Theory Seminar\n\n\nAbstract\nThe set $A$ is a 
 $B_h$-set if every element of the sumset $hA$ has a unique representation 
 as a sum of $h$ elements of $A$.  A $B_2$-set is also called a Sidon set. 
  A $B_{h\,\\Delta}$-set is a $B_h$-set $A$ whose sumset $hA$ is $\\Delta$-
 separated\, that is\, \n$x'-x \\geq \\Delta$ for all $x\,x' \\in hA$ with 
 $x < x'$.\nUpper and lower bounds are obtained for the cardinality of the 
 largest $B_{2\,\\Delta}$-sets contained in   $\\{1\,2\,\\ldots\, n\\}$\, t
 hat is\, sets $A \\subseteq \\{1\,2\,\\ldots\, n\\}$ such that\, if $a\,b\
 ,c\,d \\in A$ and $\\{a\,b\\} \\neq \\{c\,d\\}$\, then $|(a+b)-(c+d)| \\ge
 q \\Delta$.\n
LOCATION:/talk/NYNTS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mel Nathanson (CUNY)
DTSTART:20260917T190000Z
DTEND:20260917T200000Z
DTSTAMP:20260906T220842Z
UID:NYNTS/2
DESCRIPTION:Title: <a href="https://master.researchseminars.org/talk/NYNTS
 /2/">B_h-sets and perturbations in normed vector spaces</a>\nby Mel Nathan
 son (CUNY) as part of New York Number Theory Seminar\n\n\nAbstract\nThe su
 bset $A = \\{a_i:i \\in I\\}$ of a normed vector space is a $B_h$-set if e
 very element \nof the sumset $hA$ has a unique representation as a sum of 
 $h$ elements of $A$.  \nAn $\\varepsilon$-perturbation of $A$ is a set $A'
  = \\{a'_i:i\\in I\\}$ such that $|a'-a|<\\varepsilon$ \nfor all $i \\in I
 $. \nLet $\\Delta_{hA} = \\inf\\{|x'-x| : x\,x' \\in hA \\text{ and } x\\n
 eq x'\\}$.  \nIt is proved that if $A$ is  finite or countably infinite se
 t with $\\Delta_{hA}>0$\, \nthen there is a $B_h$-set $A'$ that is an $\\v
 arepsilon$-perturbation of $A$.\n
LOCATION:/talk/NYNTS/2/
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