Young diagram

Definition

A Young diagram is a finite set $D \subseteq \mathbb{N} \times \mathbb{N}$ with this property: if $(i, j) \in D$ , $i' \le i$ and $j' \le j$ , then $(i', j') \in D$ . The elements of $D$ are the cells, or boxes, of the diagram. A cell $(i, j)$ is drawn as a unit square in row $i$ and column $j$ , with rows numbered from the top.

Remarks

The rows of a Young diagram have weakly decreasing lengths $\lambda_1 \ge \lambda_2 \ge \dots$ . Thus a Young diagram with $n$ cells is the same as a partition of $n$ . This drawing convention is the English one. The French convention draws row $0$ at the bottom. Transposing a diagram, $(i, j) \mapsto (j, i)$ , gives the diagram of the conjugate partition.

Reading path

To understand this page from the ground up, read these 2 pages in order. The foundations come first.

Show the path as a graph

Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.

no evidence level

Integer partition definition
Young diagram definition

Tag	`0K78D81EF7`
URI	`m2://0K78D81EF7`
Kind	definition
Writing	W0 stub
MSC	05A17
Defines	Young diagram
Uses	Integer partition

Young diagram

Definition

Remarks

Reading path

Further reading

What this page needs for W1

What links here