LatticePaths

The monotone lattice paths from $(0,0)$ to $(a,b)$ using unit north/east steps, each written as a $0/1$ step sequence ($1$ = north). Count $\binom{a+b}{a}$.

✓ checked against that system · ! checked, with disagreements (hover a chip)OEISA046899✓↗

LatticePaths(a, b)the monotone north/east lattice paths in an $a \times b$ grid

Typed signatures

Type	Package	Applies
(integer<0..>, integer<0..>) -> indexed_collection<list<integer>>	combinatorics	always

Domain: Collections

Examples

Basic #

$\binom{5}{3} = 10$

live ↗

In$\mathrm{Count}(\mathrm{LatticePaths}(3, 2))$Out$10$

$1$ = north

live ↗

In$\mathrm{Take}(\mathrm{LatticePaths}(2, 2), 6)$Out$\bigl\lbrack\bigl\lbrack1, 1, 0, 0\bigr\rbrack, \bigl\lbrack1, 0, 1, 0\bigr\rbrack, \bigl\lbrack0, 1, 1, 0\bigr\rbrack, \bigl\lbrack1, 0, 0, 1\bigr\rbrack, \bigl\lbrack0, 1, 0, 1\bigr\rbrack, \bigl\lbrack0, 0, 1, 1\bigr\rbrack\bigr\rbrack$

About

Examples	2
Crosswalk	OEIS

See also: PartitionsInBox