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Four Numerical Triangles in Nexus

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Visit this site: http://www.math.uaa.alaska.edu/~smiley/numbertriangle.html

Author:Len Smiley
Description: Three well-known combinatorial number triangles are tightly related to each other as coefficients in transforms of a seminal sequence of exponential generating functions (for n^{n+m}). A fourth triangle is a part of the picture in much the same way that the "forgotten symmetric functions" adhere to the complete, the monomial, and the power sums. Also, Carlitz-Riordan Identities (with tables for Second-order Eulerian and Second-order Stirling numbers), Gessel and Stanley multiset permutations (GS-Permutations), Golliwog Numbers (featuring tables and a formula for the numbers called "differences of reciprocal powers of unity"), Pez story problem, and Completion of a Sequence of Carlitz.

Levels: High School (9-12), College
Languages: English
Resource Types: Problems/Puzzles
Math Topics: Combinatorics, Triangles and Other Polygons, Sequences and Sets

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