BEGIN:VCALENDAR
CALSCALE:GREGORIAN
PRODID:iCalendar-Ruby
VERSION:2.0
BEGIN:VEVENT
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.facetsofcomplexity.de
URL:http://www.facetsofcomplexity.de/monday/20210705-L-Sissokho.html
END:VEVENT
END:VCALENDAR