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DESCRIPTION: A polyhedron defined by an integral valued constraint matrix a
nd an integral valued right-hand side is lattice-free if it does not contai
n an element of the integer lattice. In this talk\, we present a link betwe
en the lattice-freeness of polyhedra\, the diameter of finite abelian group
s and the height of Hilbert bases. As a result\, we will be able to prove n
ovel upper bounds on the lattice width of lattice-free pyramids if a conjec
ture regarding the height of Hilbert bases holds. Further\, we improve exis
ting lattice width bounds of lattice-free simplices. All our bounds are ind
ependent of the dimension and solely depend on the maximal minors of the co
nstraint matrix. The second part of the talk is devoted to a study of the
above-mentioned conjecture. We completely characterize the Hilbert basis o
f a pointed polyhedral cone when all the maximal minors of the constraint m
atrix are bounded by two in absolute value. This can be interpreted as an e
xtension of a well-known result which states that the Hilbert basis element
s lie on the extreme rays if the constraint matrix is unimodular\, i.e.\, a
ll maximal minors are bounded by one in absolute value. This is joint wor
k with Martin Henk and Robert Weismantel.
DTSTAMP:20211110T180500
DTSTART:20211115T160000
CLASS:PUBLIC
LOCATION:online via Zoom\n
SEQUENCE:0
SUMMARY:Stefan Kuhlmann (Technische Universität Berlin): Lattice width of l
attice-free polyhedra and height of Hilbert bases
UID:107919476@www.facetsofcomplexity.de
URL:http://www.facetsofcomplexity.de/monday/20211115-C-Kuhlmann.html
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