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词汇 Lattice Path
分类 英语词汇 英语翻译词典
释义

Lattice Path

英语百科

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 .
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