From Binomial to Trinomial Coefficients and Beyond
In [3 (Chapter 6, Part I), 5, and 6] we presented the binomial coefficients r n in a geometric, an algebraic, and a combinatorial framework, being much concerned with establishing interesting connections between their algebraic properties and geometric features of the Pascal Triangle.
KeywordsEquilateral Triangle Multinomial Coefficient Binomial Coefficient Regular Tetrahedron Combinatorial Interpretation
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- 1.Aldred, Robert, Peter Hilton, Derek Holton, and Jean Pedersen, Baked Beans and Spaghetti, The Mathematics Educator 5, No. 2 (1994), 35–41.Google Scholar
- 3.Hilton, Peter, Derek Holton, and Jean Pedersen, Mathematical Reflections — In a Room with Many Mirrors, 2nd printing, Springer Verlag NY, 1998.Google Scholar
- 5.Hilton, Peter, and Jean Pedersen, Relating geometry and algebra in the Pascal triangle, hexagon, tetrahedron, and cuboctahedron. Part I: Binomial coefficients, extended binomial coefficients and preparation for further work, The College Mathematics Journal, 30, No. 3 (1999), 170–186.MathSciNetMATHCrossRefGoogle Scholar
- 6.Hilton, Peter, and Jean Pedersen, Relating geometry and algebra in the Pascal triangle, hexagon, tetrahedron, and cuboctahedron. Part II: Geometry and algebra in higher dimensions: Identifying the Pascal cuboctahedron, The College Mathematics Journal, 30, No. 4 (1999), 279–292.MathSciNetMATHCrossRefGoogle Scholar
- 8.Hilton, Peter, and Shaun Wylie, Homology Theory, Cambridge University Press, 3rd printing, 1965.Google Scholar