Integer hulls of linear polyhedra and scl in families

Details Integer hulls of linear polyhedra and scl in families Integer hulls of linear polyhedra and scl in families

2010-11-05

arxiv.org/abs/1011.1455v3

Mathematics

Combinatorics

18 pages, 3 figures; v3 includes referee's suggestions

Scientific paper

The integer hull of a polyhedron is the convex hull of the integer points contained in it. We show that the vertices of the integer hulls of a rational family of polyhedra of size O(n) have quasipolynomial coordinates. As a corollary, we show that the stable commutator length of elements in a surgery family is a ratio of quasipolynomials, and that unit balls in the scl norm quasi-converge in finite dimensional surgery families.

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