44/365 - D is for Design

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D is for Design, whose Theory I study -- along with the Codes, the Finite Geometries, and the Graphs. What is a Design? It's a particular type of Combinatorial structure. Here's the formal definition:

A t-(v, k, L) design D is a set of v points and k-subsets of the points called blocks. Each t-subset of the points must appear in exactly L blocks.

Informally, a Design is a bunch of "points" (usually numbers), organized into chunks of points called "blocks" (which may overlap with each other). Each block has the same number of points in it, and each smaller set of points (t points) must appear in the same number of blocks. This is the "fairness" condition, meaning that the points are distributed "evenly" among the blocks. They are used commonly in planning statistical experiments, and also as links to other types of combinatorics.