Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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A DIOPHANTINE CONSTRUCTION OF AN EXACT ALGEBRAIC FORMULA FOR GRADED PARTITION FUNCTIONS

  • Soh, Sun-T. (Department of Mathematics MyongJi University)
  • Published : 1999.03.01
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Abstract

A geometric construction of an exact algebraic formula for graded partition functions, of which a special one is the classical unrestricted partition function p(n), from a diophantine point of view is presented. Moreover, the involved process allows us to compute the value of a graded partition function in an inductive manner with a geometrically built-in self-error-checking ability at each step for correctness of the computed values of the partition function under consideration.

Keywords

References

  1. Number Theory G. E. Andrews
  2. The Theory of Partitions (2nd printing) G. E. Andrews
  3. Romanujan's Notebooks B. C. Berndt
  4. A First Course, GTM129 Representation Theory W. Fulton;J. Harris
  5. Topics from the Theory of Numbers E. Grosswald
  6. An Introduction to the Theory of Numbers (5th Ed) G. H. Hardy;E. M. Wright
  7. Topics in Algebra (2nd Ed) I. N. Herstein
  8. Encyclopedic Dictionary of Mathematics (2nd Ed.) v.2 Math. Soc. of Japan
  9. An Introduction to the Theory of Numbers (5th Ed.) I. Niven (et al.)
  10. J. Math. Assoc v.81 no.490 Computations of the partition function, The Mathematical Gazette P. Shiu
  11. Enumerative Combinatorics v.I R. P. Stanley
  12. Texts and Monographs in Symbolic Computation Algorithms in Invariant Theory B. Sturmfels
  13. RIM-GARC Preprint Series 95-15, Research Institute of Math. On a Complete Intersection Sun T. Soh
  14. (Quasi-) Recursive Formulas for Graded Partition Functions Sun T. Soh
  15. Efficient Formulas for the Coefficients of the Gaussian Polynomials$\frac{n}{m}$