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Lattice path of length 5 in ℤ 2 with S = { (2,0), (1,1), (0,-1) }.. In combinatorics, a lattice path L in the d-dimensional integer lattice of length k with steps in the set S, is a sequence of vectors ,, …, such that each consecutive difference lies in S. [1]
A bounded lattice is a lattice. (def) 13. A heyting algebra is residuated. 14. A residuated lattice is a lattice. (def) 15. A distributive lattice is modular. [3] 16. A modular complemented lattice is relatively complemented. [4] 17. A boolean algebra is relatively complemented. (1,15,16) 18. A relatively complemented lattice is a lattice. (def ...
In mathematics, the Schröder number, also called a large Schröder number or big Schröder number, describes the number of lattice paths from the southwest corner (,) of an grid to the northeast corner (,), using only single steps north, (,); northeast, (,); or east, (,), that do not rise above the SW–NE diagonal.
C n is the number of monotonic lattice paths along the edges of a grid with n × n square cells, which do not pass above the diagonal. A monotonic path is one which starts in the lower left corner, finishes in the upper right corner, and consists entirely of edges pointing rightwards or upwards.
Pages in category "Lattice points" The following 39 pages are in this category, out of 39 total. This list may not reflect recent changes. ...
In mathematics, a self-avoiding walk (SAW) is a sequence of moves on a lattice (a lattice path) that does not visit the same point more than once. This is a special case of the graph theoretical notion of a path. A self-avoiding polygon (SAP) is a closed self-avoiding walk on a lattice. Very little is known rigorously about the self-avoiding ...
An n-path from an n-tuple (,, …,) of vertices of G to an n-tuple (,, …,) of vertices of G will mean an n-tuple (,, …,) of paths in G, with each leading from to . This n -path will be called non-intersecting just in case the paths P i and P j have no two vertices in common (including endpoints) whenever i ≠ j {\displaystyle i\neq j} .
The degree of translation is then added as a subscript showing how far along the axis the translation is, as a portion of the parallel lattice vector. For example, 2 1 is a 180° (twofold) rotation followed by a translation of 1 / 2 of the lattice vector. 3 1 is a 120° (threefold) rotation followed by a translation of 1 / 3 of ...