The Reflection Lemma
The Reflection Lemma is concerned with counting the number of random walks that satisfy certain conditions. It is quite common to denote the number of walks from
What if applet does not run? |
The Reflection Lemma
For a > 0, b > 0,
Mn(a, b) = Nn(-a, b),
where Mn(a, b) is the number of walks from
The applet provides a graphical illustration for a proof of the Reflection Lemma. Let
The applet actually illustrates the Lemma for walks from
References
- W. Feller, An Introduction to Probability Theory and Its Applications, Vol. 1, 3rd Edition, Wiley, 1968

Pascal's Triangle and the Binomial Coefficients
- Binomial Theorem
- Arithmetic in Disguise
- Construction of Pascal's Triangle
- Dot Patterns, Pascal Triangle and Lucas Theorem
- Integer Iterations on a Circle
- Leibniz and Pascal Triangles
- Lucas' Theorem
- Lucas' Theorem II
- Patterns in Pascal's Triangle
- Random Walks
- The Ballot Lemma
- The Reflection Lemma
- Sierpinski Gasket and Tower of Hanoi
- Treatise on Arithmetical Triangle
- Ways To Count
- Another Binomial Identity with Proofs
- Vandermonde's Convolution Formula
- Counting Fat Sets
- e in the Pascal Triangle
- Catalan Numbers in Pascal's Triangle
- Sums of Binomial Reciprocals in Pascal's Triangle
- Squares in Pascal's Triangle
- Cubes in Pascal's Triangle
- Pi in Pascal's Triangle
- Pi in Pascal's Triangle via Triangular Numbers
- Ascending Bases and Exponents in Pascal's Triangle
- Determinants in Pascal's Triangle
- Tony Foster's Integer Powers in Pascal's Triangle

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