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Macmahon's partition analysis IX: K-gon partitions

Published online by Cambridge University Press:  17 April 2009

George E. Andrews ,
Peter Paule  and
Axel Riese
George E. Andrews
Affiliation:
Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, United States of America, e-mail: andrews@math.psu.edu
Peter Paule
Affiliation:
Research Institute for Symbolic Computation, Johannes Kepler University Linz, A–4040 Linz, Austria, e-mail: Peter.Paule@risc.uni-linz.ac.at
Axel Riese
Affiliation:
Research Institute for Symbolic Computation, Johannes Kepler University Linz, A–4040 Linz, Austria, e-mail: Axel.Riese@risc.uni-linz.ac.at
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Dedicated to George Szekeres on the occasion of his 90th birthday

MacMahon devoted a significant portion of Volume II of his famous book Combinatory Analysis to the introduction of Partition Analysis as a computational method for solving combinatorial problems in connection with systems of linear diophantine inequalities and equations. In a series of papers we have shown that MacMahon's method turns into an extremely powerful tool when implemented in computer algebra. In this note we explain how the use of the package Omega developed by the authors has led to a generalisation of a classical counting problem related to triangles with sides of integer length.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 64 , Issue 2 , October 2001 , pp. 321 - 329
Copyright
Copyright © Australian Mathematical Society 2001

References

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