TY - JOUR

T1 - An algebraic-perturbation variant of Barvinok's algorithm

AU - Lee, Jon

AU - Skipper, Daphne

N1 - Funding Information:
1 Lee was partially supported by NSF grant CMMI-1160915; ONR grant N00014-14-1-0315. 2 Email: jonxlee@umich.edu 3 Email: dapskipper@gru.edu
Publisher Copyright:
© 2015 Elsevier B.V.

PY - 2015/12/1

Y1 - 2015/12/1

N2 - We give a variant of Barvinok's algorithm for computing a short rational generating function for the integer points in P := {x ∈ Rn : Ax ≤ b}; a use of which is to count the number of integer points in P. We use an algebraic perturbation, replacing each bi with bi+τi, where τ>0 is an arbitrarily small indeterminate. Hence, our new right-hand vector has components in the ordered ring Q[τ] of polynomials in τ. Denoting the perturbed polyhedron by P(τ)⊂R[τ]n, we use the facts that: P(τ) is full dimensional, simple, and contains the same integer points as P.

AB - We give a variant of Barvinok's algorithm for computing a short rational generating function for the integer points in P := {x ∈ Rn : Ax ≤ b}; a use of which is to count the number of integer points in P. We use an algebraic perturbation, replacing each bi with bi+τi, where τ>0 is an arbitrarily small indeterminate. Hence, our new right-hand vector has components in the ordered ring Q[τ] of polynomials in τ. Denoting the perturbed polyhedron by P(τ)⊂R[τ]n, we use the facts that: P(τ) is full dimensional, simple, and contains the same integer points as P.

KW - Barvinok's algorithm

KW - Generating function

KW - Integer

KW - Polyhedron

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U2 - 10.1016/j.endm.2015.07.004

DO - 10.1016/j.endm.2015.07.004

M3 - Article

AN - SCOPUS:84953378005

SN - 1571-0653

VL - 50

SP - 15

EP - 20

JO - Electronic Notes in Discrete Mathematics

JF - Electronic Notes in Discrete Mathematics

ER -