Free polygon enumeration and the area of an integral polygon,
Discrete Mathematics, 218 (2000), 109-119.
An Euler-type formula is derived for the number of integer points in
the interior of an integral polygon; that is, a polygon with vertices
having integer coordinates. This leads in turn to a formula for the
area of an integral polygon P via the enumeration of free
integral triangles and parallelograms contained inside P. This
paper presents a purely combinatorial (and fairly elementary) approach
to some interesting special cases of the more general results in
An Euler relation for valuations on
polytopes.
A pdf file for this paper is available
here.
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