935 research outputs found
Foam evaluation and Kronheimer--Mrowka theories
We introduce and study combinatorial equivariant analogues of the
Kronheimer--Mrowka homology theory of planar trivalent graphs.Comment: 53 pages, 23 tikz figure
Inside-Out Polytopes
We present a common generalization of counting lattice points in rational
polytopes and the enumeration of proper graph colorings, nowhere-zero flows on
graphs, magic squares and graphs, antimagic squares and graphs, compositions of
an integer whose parts are partially distinct, and generalized latin squares.
Our method is to generalize Ehrhart's theory of lattice-point counting to a
convex polytope dissected by a hyperplane arrangement. We particularly develop
the applications to graph and signed-graph coloring, compositions of an
integer, and antimagic labellings.Comment: 24 pages, 3 figures; to appear in Adv. Mat
- …