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SUMMARY:Shalom Eliahou (Universit\\'e du Littoral C\\^ote d'Opale\, Calais
 \, France)
DTSTART:20260326T190000Z
DTEND:20260326T203000Z
DTSTAMP:20260427T053100Z
UID:New_York_Number_Theory_Seminar/132
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/New_York_Num
 ber_Theory_Seminar/132/">On Wilf's conjecture for numerical semigroups</a>
 \nby Shalom Eliahou (Universit\\'e du Littoral C\\^ote d'Opale\, Calais\, 
 France) as part of New York Number Theory Seminar\n\n\nAbstract\nA numeric
 al semigroup $S$ is a cofinite submonoid of $\\mathbb{N}$. This means that
  $S$ is stable under addition\, contains $0$\, and has finite complement i
 n $\\mathbb{N}$. Some important numbers attached to $S$ are its genus $g =
  \\text{card}(\\mathbb{N} \\setminus S)$\, its conductor $c=\\max(\\mathbb
 {Z} \\setminus S)+1$ and its minimal number $n$ of generators. Half a cent
 ury ago\, Herbert Wilf came up with a very clever conjectural upper bound 
 on the genus $g$ in terms of $c$ and $n$\, namely \n$$g \\le c(1-1/n).$$\n
 In this talk\, we will provide a brief overview of the current status of W
 ilf's conjecture and discuss connections with additive combinatorics\, gra
 ph theory and commutative algebra.\n
LOCATION:https://researchseminars.org/talk/New_York_Number_Theory_Seminar/
 132/
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