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  "body": "\n## Summary\n\nA lattice path is a finite sequence of points of the integer lattice $\\mathbb{Z}^2$. Each step between consecutive points is from a given finite set of steps.\nThe most common case uses the steps $E = (1, 0)$ and $N = (0, 1)$. These are North-East lattice paths.\n\nA North-East path from $(0, 0)$ to $(a, b)$, with $a, b \\in \\mathbb{N}$, has $a$ steps $E$ and $b$ steps $N$.\nIt is a word of length $a + b$ in $E$ and $N$. Thus the number of such paths is the [[binomial coefficient|092GEF38YD]] $\\binom{a + b}{a}$.\n\n## Remarks\n\nThe number of North-East paths from $(0, 0)$ to $(n, n)$ is the [[central binomial coefficient|01WHD9T0V6]] $\\binom{2n}{n}$.\nThe paths of this type that never go above the diagonal $y = x$ are counted by the [[Catalan numbers|092DRBFKMG]]. They correspond to [[Dyck words|0R9JR0465V]].\n\n## Explanations\n\n### L1 human\n\nThink of a city grid where you may only walk east or north.\nTo go 3 blocks east and 2 blocks north, you choose which 2 of your 5 steps go north, so there are $\\binom{5}{2} = 10$ routes.\n",
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