Journal of Algebraic Combinatorics

, Volume 22, Issue 3, pp 331–341 | Cite as

Counting Monomials

  • Mordechai Katzman


This paper presents two enumeration techniques based on Hilbert functions. The paper illustrates these techniques by solving two chessboard problems.


Hilbert function chessboard problem 


  1. 1.
    W.W. Adams and P. Loustaunau, An Introduction to Gröbner Bases, Graduate Studies in Mathematics, 3, American Mathematical Society, Providence, RI, 1994.Google Scholar
  2. 2.
    W.W. Rouse Ball, Mathematical Recreations & Essays, Macmillan, London, 1940.Google Scholar
  3. 3.
    M. Gardner, A Gardner's Workout, A K Peters, Ltd., Natick, MA, 2001.Google Scholar
  4. 4.
    GS D. Grayson and M. Stillman, Macaulay 2–a Software System for Algebraic Geometry and Commutative Algebra, Available at Scholar
  5. 5.
    M. Katzman, FreeSquares Available from Scholar
  6. 6.
    F.S. Macaulay, “Some properties of enumeration in the theory of modular systems,” Proceedings of the London Mathematical Society 26, 531–555.Google Scholar
  7. 7.
    B. Sturmfels, Gröbner Bases and Convex Polytopes, University Lecture Series, 8. American Mathematical Society, Providence, RI, 1996.Google Scholar
  8. 8.
    Richard P. Stanley, Combinatorics and Commutative Algebra, Second edition. Progress in Mathematics, 41. Birkhäuser Boston, Inc., Boston, MA, 1996.Google Scholar

Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Department of Pure MathematicsUniversity of SheffieldSheffieldUK

Personalised recommendations