volume 32, issue 4, P437-446 2004
DOI: 10.1007/s00454-004-1131-5
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Abstract: Dedicated to Lou Billera on the occasion of his sixtieth birthday.Abstract. We present a new tool to compute the number φA(b) of integer solutions to the linear system x ≥ 0 , A x = b , where the coefficients of A and b are integral. φA(b) is often described as a vector partition function. Our methods use partial fraction expansions of Euler's generating function for φA(b). A special class of vector partition functions are Ehrhart (quasi-)polynomials counting integer points in dilated polytopes. Euler's gener…

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