enumeratio

@enumeratio/diagram ​

Diagram-algebra extensions for compute-engine: the partition algebra and its subalgebras (Brauer, Temperley–Lieb, Motzkin, rook, symmetric group), whose bases are combinatorial diagrams — set partitions of a top and bottom row, multiplied by stacking and gluing. The construction, the lattice of subalgebras and the dimension formulas are in the guide.

Declaring ​

ts
import { ComputeEngine } from "@cortex-js/compute-engine";
import { declareDiagrams } from "@enumeratio/diagram";

const ce = new ComputeEngine();
declareDiagrams(ce);

Heads ​

src/dimensions.ts also exports the closed-form counts behind AlgebraDimension — bell, catalan, motzkin, rookCount — and src/orbit.ts the coarsening machinery for InOrbitBasis.

Usage ​

AlgebraDimension(PartitionAlgebra(3))          // 203 — B(6), the Bell number
AlgebraDimension(PlanarPartitionAlgebra(3))    // 132 — planarity cuts 203 down to C(6)
Element(Diagram([[1, 2, -1], [3, -3], [-2]]), PartitionAlgebra(3))   // True

Next ​

The guide covers which subalgebra corresponds to which restriction on admitted diagrams (planar, non-crossing, fixed-point-free, …) and how a closed loop contributes the loop parameter δδ on multiplication.

Pages ​