This is the first text to collect and organize the current research on triangular arrays and their applications. An invaluable resource book, it gives a historical introduction to Pascal's triangle and covers application topics such as binomial coefficients, figurate numbers, Fibonacci and Lucas numbers, Pell and Pell-Lucas numbers, graph theory, Fibonomial and tribinomial coefficients and Fibonacci and Lucas polynomials.
Inhaltsverzeichnis
- Contents
- Preface
- 1.: Fundamentals
- 2.: Binomial Coefficients
- 3.: The Binomial Theorem
- 4.: Binomial Congruences
- 5.: Binomial Coefficients Revisited
- 6.: Pascal's Triangle
- 7.: Pascal's Triangle Revisited
- 8.: Pascal's m-ary Triangles
- 9.: Pascal Graphs
- 10.: Maclaurin's Series
- 11.: Fibonacci and Lucas Numbers
- 12.: Pascal's Triangle and Generating Functions
- 13.: Pascal-like Triangles
- 14.: Fibonacci Triangles
- 15.: Josef 's Triangle
- 16.: Lucas Triangles
- 17.: Catalan Numbers and Pascal's Triangle
- 18.: Catalan's Parenthesization Problem Revisited
- 19.: Leibniz's Harmonic Triangle
- 20.: Stirling's Triangles
- 21.: Bell's Triangles
- 22.: Euler's Triangles
- 23.: Lah's Triangle
- 24.: Fibonacci Convolution Triangles
- 25.: Tartaglia's Arrays
- 26.: Miscellaneous Arrays
- 27.: Tribinomial Triangles
- 28.: Fibonomial Triangles
- 29.: Multinomial Arrays
