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SUMMARY:Pierre-Yves Bienvenu (Universite de Lyon)
DTSTART:20200601T170000Z
DTEND:20200601T172500Z
DTSTAMP:20260423T011111Z
UID:CANT2020/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2020/7/"
 >Additive bases in infinite abelian semigroups\, I</a>\nby Pierre-Yves Bie
 nvenu (Universite de Lyon) as part of Combinatorial and additive number th
 eory (CANT 2021)\n\n\nAbstract\nAn additive basis $A$  of a semigroup $T$ 
 is a subset such that every element of $T$\, \nup to a finite set of excep
 tions\, may be written as a sum of one and the same number \n$h$ of elemen
 ts from the basis.  The minimal such number $h$ is called the order of the
  basis. \nWe study bases in a class of infinite abelian semigroups\, which
  we term translatable semigroups. \nThese include all infinite abelian gro
 ups as well as the semigroup of nonnegative integers.  \nWe analyze the ``
 robustness" of bases. \nSuch discussions have a long history in the semigr
 oup ${\\mathbf N}$\, \noriginating in the work of Erd\\H os and Graham\, c
 ontinued by Deschamps and Farhi\, \nNathanson and Nash\, Hegarty....  Thus
  we consider essential subsets of a basis $A$\, \nthat is\, finite sets $F
 $ such that $A \\setminus F$ \nis no longer a basis\, and which are minima
 l. We show that any basis has only finitely \nmany essential subsets\, and
  we bound the number of essential subsets of cardinality $k$ \nof a basis 
 of order $h$ in terms of $h$ and $k$. \n\nJoint work with Benjamin Girard 
 and Thai Hoang Lˆe.\n
LOCATION:https://researchseminars.org/talk/CANT2020/7/
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