LinearQuiver

The quiver $A_n$: $1 \to 2 \to \cdots \to n$, acyclic, whose path algebra is the incidence algebra of a chain.

LinearQuiver(n)the chain quiver $1\to2\to\cdots\to n$

Typed signatures

Type	Package	Applies
(integer) -> expression<LinearQuiver>	quiver	always

Domain: Path algebras

Examples

Basic #

live ↗

In$\mathrm{QuiverIsAcyclic}(\mathrm{LinearQuiver}(4))$Out$\mathrm{True}$

$\binom{7}{2}$ paths

live ↗

In$\mathrm{AlgebraDimension}(\mathrm{PathAlgebra}(\mathrm{LinearQuiver}(6)))$Out$21$

About

Examples	2

See also: Quiver, QuiverIsAcyclic, PathAlgebra