Block walking

In combinatorial mathematics, block walking is a method useful in thinking about sums of combinations graphically as "walks" on Pascal's triangle. ^[1]

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Table of Contents

1. 7 relations: Combinatorial proof, Combinatorics, Lattice (group), Lattice path, Origin (mathematics), Pascal's triangle, Proof by exhaustion.

Combinatorial proof

In mathematics, the term combinatorial proof is often used to mean either of two types of mathematical proof.

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Combinatorics

Combinatorics is an area of mathematics primarily concerned with the counting, selecting and arranging of objects, both as a means and as an end in itself.

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Lattice (group)

In geometry and group theory, a lattice in the real coordinate space \mathbb^n is an infinite set of points in this space with the properties that coordinate-wise addition or subtraction of two points in the lattice produces another lattice point, that the lattice points are all separated by some minimum distance, and that every point in the space is within some maximum distance of a lattice point.

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Lattice path

In combinatorics, a lattice path in the -dimensional integer lattice of length with steps in the set, is a sequence of vectors such that each consecutive difference v_i - v_ lies in.

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Origin (mathematics)

In mathematics, the origin of a Euclidean space is a special point, usually denoted by the letter O, used as a fixed point of reference for the geometry of the surrounding space.

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Pascal's triangle

In mathematics, Pascal's triangle is an infinite triangular array of the binomial coefficients which play a crucial role in probability theory, combinatorics, and algebra.

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Proof by exhaustion

Proof by exhaustion, also known as proof by cases, proof by case analysis, complete induction or the brute force method, is a method of mathematical proof in which the statement to be proved is split into a finite number of cases or sets of equivalent cases, and where each type of case is checked to see if the proposition in question holds.

See Block walking and Proof by exhaustion

References

[1] https://en.wikipedia.org/wiki/Block_walking

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