Explore relationships

Lattice path

In combinatorics, a lattice path L in the d-dimensional integer lattice ⁠ Z d {\displaystyle \mathbb {Z} ^{d}} ⁠ of length k with steps in the set S, is a sequence of vectors ⁠ v 0 , v 1 , … , v k ∈ Z d {\displaystyle v_{0},v_{1},\ldots ,v_{k}\in \mathbb {Z} ^{d}} ⁠ such that each consecutive difference v i − v i − 1 {\displaystyle v_{i}-v_{i-1}} lies in S. A lattice path may lie in any lattice in ⁠ R d {\displaystyle \mathbb {R} ^{d}} ⁠, but the integer lattice ⁠ Z d {\displaystyle \mathbb {Z} ^{d}} ⁠ is most commonly used.

Use + to expand a branch. Click a topic name to open its summary.