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2. Lattice path - Wikipedia

   en.wikipedia.org/wiki/Lattice_Path

   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]

3. Lindström–Gessel–Viennot lemma - Wikipedia

   en.wikipedia.org/wiki/Lindström–Gessel...

   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} .

4. Map of lattices - Wikipedia

   en.wikipedia.org/wiki/Map_of_lattices

   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) 19. A heyting algebra is distributive. [5] 20. A totally ordered set is a ...

5. Schröder number - Wikipedia

   en.wikipedia.org/wiki/Schröder_number

   The (large) Schröder numbers count both types of paths, and the little Schröder numbers count only the paths that only touch the diagonal but have no movements along it. [ 3 ] Just as there are (large) Schröder paths, a little Schröder path is a Schröder path that has no horizontal steps on the x {\displaystyle x} -axis.

6. Self-avoiding walk - Wikipedia

   en.wikipedia.org/wiki/Self-avoiding_walk

   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 ...

7. Narayana number - Wikipedia

   en.wikipedia.org/wiki/Narayana_number

   In the study of partitions, we see that in a set containing ⁠ ⁠ elements, we may partition that set in different ways, where is the ⁠ ⁠ th Bell number. Furthermore, the number of ways to partition a set into exactly ⁠ k {\displaystyle k} ⁠ blocks we use the Stirling numbers S ( n , k ) {\displaystyle S(n,k)} .

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9. Young's lattice - Wikipedia

   en.wikipedia.org/wiki/Young's_lattice

   Since this set has both bilateral symmetry and rotational symmetry, it must have dihedral symmetry: the (n + 1)st dihedral group acts faithfully on this set. The size of this set is 2 n. For example, when n = 4, then the maximal element under the "staircase" that have rectangular Ferrers diagrams are 1 + 1 + 1 + 1 2 + 2 + 2 3 + 3 4