The partial-fractions method for counting solutions to integral linear systems
Beck, Matthias
Original · EN
We present a new tool to compute the number ϕ () of integer solutions to the linear system ≥ 0 = where the coefficients of and are integral. ϕ () is often described as a vector partition function. Our methods use partial fraction expansions of Euler's generating function for ϕ (). A special class of vector partition functions are Ehrhart (quasi-)polynomials counting integer points in dilated polytopes.
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