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SUMMARY:Wolfgang Schmid (University of Paris 8\, Saint-Denis)
DTSTART:20200601T193000Z
DTEND:20200601T195500Z
DTSTAMP:20260423T011239Z
UID:CANT2020/12
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2020/12/
 ">Plus-minus weighted zero-sum sequences and applications to factorization
 s of norms of quadratic integers</a>\nby Wolfgang Schmid (University of Pa
 ris 8\, Saint-Denis) as part of Combinatorial and additive number theory (
 CANT 2021)\n\n\nAbstract\nLet $(G\,+)$ be a finite abelian group. A sequen
 ce $g_1\, \\dots\, g_k$ over $G$ \nis called a zero-sum sequence if $g_1 +
  \\dots + g_k = 0$ \n(we consider sequences that just differ by the orderi
 ng of the terms as equal).   \nThe concatenation of two zero-sum sequences
  is a zero-sum sequence and the set \nof all zero-sum sequences over $G$ i
 s thus a monoid. The arithmetic of these monoids \nhas been the subject mu
 ch investigation. \n\nA sequence is called a \\emph{plus-minus weighted ze
 ro-sum sequence} if there is a choice \nof weights $w_i \\in \\{-1\, +1\\}
 $ such that \n$w_1g_1 + \\dots + w_k g_k = 0$. The set of all plus-minus w
 eighted zero-sum sequences \nover $G$ is a monoid as well.\nWe present som
 e results on the arithmetic of these monoids.\nMoreover\, applications to 
 factorizations of norms of quadratic integers are discussed. \n\nJoint wor
 k with S. Boukheche\, K. Merito and O. Ordaz.\n
LOCATION:https://researchseminars.org/talk/CANT2020/12/
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