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DESCRIPTION: Let a 1 \,...\,a n  and b 1 \,...\,b m  be fixed positive inte
 gers\, and let S denote the set of all nonnegative integer solutions of the
  equation x 1 a 1 +...+x n a n =y 1 b 1 +...+y m b m . A solution (x 1 \,..
 .\,x n \,y 1 \,...\,y m ) in S is called  minimal  if it cannot be expresse
 d as the sum of two nonzero solutions in S.  For each pair (i\,j)\, with 1 
 ≤ i ≤ n and 1 ≤ j ≤ m\, the solution whose only nonzero coordinates are x i
   = b j  and y j  = a i  is called a  generator .  We show that every minim
 al solution is a convex combination of the generators and the zero-solution
 . This proves a conjecture of Henk-Weismantel and\, independently\, Hosten-
 Sturmfels. 
DTSTAMP:20210629T164900
DTSTART:20210705T141500
CLASS:PUBLIC
LOCATION:online
SEQUENCE:0
SUMMARY:Papa Sissokho (Illinois State University): Geometry of the minimal 
 Solutions of a linear diophantine Equation
UID:107919111@/www.mi.fu-berlin.de
URL:https://www.mi.fu-berlin.de/en/facetsofcomplexity/monday/20210705-L-Sis
 sokho.html
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