Integer Programming, Combinatorics, and Splines

  • David Cox
  • John Little
  • Donal O’Shea
Part of the Graduate Texts in Mathematics book series (GTM, volume 185)


In this chapter we will consider a series of interrelated topics concerning polyhedral regions P in ℝ n , the integer points in these regions, and piece-wise polynomial functions on subdivisions of such regions. In each case Gröbner basis techniques give important computational and conceptual tools to deal with problems of interest and practical importance. These topics are also closely related to the material on polytopes and toric varieties from Chapter 7, but we have tried to make this chapter as independent as possible from Chapter 7 so that it can be read separately.


Integer Program Feasible Region Toric Variety Spline Function Hilbert Series 
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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • David Cox
    • 1
  • John Little
    • 2
  • Donal O’Shea
    • 3
  1. 1.Department of Mathematics and Computer ScienceAmherst CollegeAmherstUSA
  2. 2.Department of MathematicsCollege of the Holy CrossWorcesterUSA
  3. 3.Department of Mathematics, Statistics and Computer ScienceMount Holyoke CollegeSouth HadleyUSA

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