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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…

Counting lattice paths, General references & Combinations and NE lattice paths

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Counting lattice paths

BijectionCatalan numberSchröder numbersCombinations
4 related topics

General references

Narayana, Tadepalli VenkataISBNSong, ChunweiDoi
4 related topics

Combinations and NE lattice paths

Binomial coefficientPascal's triangleBijective
3 related topics

North-East lattice paths

Permutation word
1 related topics

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North-East lattice paths

Counting lattice paths

Combinations and NE lattice paths

General references

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Lattice path

Nodes23
Edges22
Triples43
Avg. degree1.91
Density0.086957
Components1

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Lattice path

Top relations

related to General references · 16
Lattice path → Boca Raton, Chunwei, CRC Press, December, Enumerative Perspective, From, ISBN, Lattice Path Combinatorics, Narayana, Song, Special Counting Sequences, Statistical Applications, Tadepalli Venkata, Toronto, Toronto Press, University
related to Counting lattice paths · 10
Lattice path → Catalan, Dyck, Equivalently, For, Lattice, NE, Similarly, The, The Schröder, This
related to North-East lattice paths · 7
Lattice path → East, Furthermore, NE, North, North-East, The, This
related to Combinations and NE lattice paths · 6
Lattice path → If, NE, Pascal's, Pascal's Triangle, The, This
related to Problems and proofs · 3
Lattice path → Here, NE, The
is a · 1
Lattice path → lattice path in Z 2

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Important terminology

lattice displaystyle paths path ne number steps mathbb lbrace rbrace combinations combinatorics set binom length word binomial coefficient example integer

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Lattice pathis alattice path in Z 20.90text
Lattice pathrelated to Combinations and NE lattice pathsNE0.60section
Lattice pathrelated to Combinations and NE lattice pathsPascal's0.60section
Lattice pathrelated to Combinations and NE lattice pathsThe0.60section
Lattice pathrelated to Combinations and NE lattice pathsIf0.60section
Lattice pathrelated to Combinations and NE lattice pathsThis0.60section
Lattice pathrelated to Combinations and NE lattice pathsPascal's Triangle0.60section
Lattice pathrelated to Counting lattice pathsLattice0.60section
Lattice pathrelated to Counting lattice pathsSimilarly0.60section
Lattice pathrelated to Counting lattice pathsThis0.60section
Lattice pathrelated to Counting lattice pathsFor0.60section
Lattice pathrelated to Counting lattice pathsDyck0.60section

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