Counting Monomials
Mordechai Katzman
University of Sheffield Department of Pure Mathematics Hicks Building Sheffield S3 7RH UK Hicks Building Sheffield S3 7RH UK
DOI: 10.1007/s10801-005-4531-6
Abstract
This paper presents two enumeration techniques based on Hilbert functions. The paper illustrates these techniques by solving two chessboard problems.
Pages: 331–341
Keywords: keywords Hilbert function; chessboard problem
Full Text: PDF
References
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5. M. Katzman, FreeSquares Available from http://www.shef.ac.uk/katzman/ComputerAlgebra/ ComputerAlgebra.html
6. F.S. Macaulay, “Some properties of enumeration in the theory of modular systems,” Proceedings of the London Mathematical Society 26, 531-555.
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2. W.W. Rouse Ball, Mathematical Recreations & Essays, Macmillan, London, 1940.
3. M. Gardner, A Gardner's Workout, A K Peters, Ltd., Natick, MA, 2001.
4. D. Grayson and M. Stillman, Macaulay 2-a Software System for Algebraic Geometry and Commutative Algebra, Available at http://www.math.uiuc.edu/Macaulay2.
5. M. Katzman, FreeSquares Available from http://www.shef.ac.uk/katzman/ComputerAlgebra/ ComputerAlgebra.html
6. F.S. Macaulay, “Some properties of enumeration in the theory of modular systems,” Proceedings of the London Mathematical Society 26, 531-555.
7. B. Sturmfels, Gr\ddot obner Bases and Convex Polytopes, University Lecture Series,
8. American Mathematical Society, Providence, RI, 1996.
8. Richard P. Stanley, Combinatorics and Commutative Algebra, Second edition. Progress in Mathematics,
41. Birkh\ddot auser Boston, Inc., Boston, MA, 1996.