Lattice path

Each NE lattice path passes through exactly one colored node.

Sets of NE lattice paths squared, with the second copy rotated 90° clockwise.

In combinatorics, a lattice path $L$ in $\mathbb{Z}^d$ of length $k$ with steps in $S$ is a sequence $v_0, v_1, \ldots, v_k \in \mathbb{Z}^d$ such that each consecutive difference $v_i - v_{i-1}$ lies in $S$ . A lattice path may lie in any lattice in $\mathbb{R}^d$ , but the integer lattice $\mathbb{Z}^d$ is most commonly used.

An example of a lattice path in $\mathbb{Z}^2$ of length 5 with steps in $S = \lbrace (2,0), (1,1), (0,-1) \rbrace$ is $L = \lbrace (-1,-2), (0,-1), (2,-1), (2,-2), (2,-3), (4,-3) \rbrace$ .

单词	Lattice Path
释义	Lattice Path 英语百科 Lattice path In combinatorics, a lattice path $L$ in $\mathbb{Z}^d$ of length $k$ with steps in $S$ is a sequence $v_0, v_1, \ldots, v_k \in \mathbb{Z}^d$ such that each consecutive difference $v_i - v_{i-1}$ lies in $S$ . A lattice path may lie in any lattice in $\mathbb{R}^d$ , but the integer lattice $\mathbb{Z}^d$ is most commonly used. An example of a lattice path in $\mathbb{Z}^2$ of length 5 with steps in $S = \lbrace (2,0), (1,1), (0,-1) \rbrace$ is $L = \lbrace (-1,-2), (0,-1), (2,-1), (2,-2), (2,-3), (4,-3) \rbrace$ .
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Lattice Path

Lattice path