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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Combinatorial design | 5/5 | https://en.wikipedia.org/wiki/Combinatorial_design | reference | science, encyclopedia | 2026-05-05T09:49:37.423591+00:00 | kb-cron |
A tuscan square on n symbols is equivalent to a decomposition of the complete graph with n vertices into n hamiltonian directed paths. In a sequence of visual impressions, one flash card may have some effect on the impression given by the next. This bias can be cancelled by using n sequences corresponding to the rows of an n × n tuscan-1 square. A t-wise balanced design (or t BD) of type t − (v,K,λ) is a v-set X together with a family of subsets of X (called blocks) whose sizes are in the set K, such that every t-subset of distinct elements of X is contained in exactly λ blocks. If K is a set of positive integers strictly between t and v, then the t BD is proper. If all the k-subsets of X for some k are blocks, the t BD is a trivial design. Notice that in the following example of a 3-{12,{4,6},1) design based on the set X = {1,2,...,12}, some pairs appear four times (such as 1,2) while others appear five times (6,12 for instance). 1 2 3 4 5 6 1 2 7 8 1 2 9 11 1 2 10 12 3 5 7 8 3 5 9 11 3 5 10 12 4 6 7 8 4 6 9 11 4 6 10 12 7 8 9 10 11 12 2 3 8 9 2 3 10 7 2 3 11 12 4 1 8 9 4 1 10 7 4 1 11 12 5 6 8 9 5 6 10 7 5 6 11 12 3 4 9 10 3 4 11 8 3 4 7 12 5 2 9 10 5 2 11 8 5 2 7 12 1 6 9 10 1 6 11 8 1 6 7 12 4 5 10 11 4 5 7 9 4 5 8 12 1 3 10 11 1 3 7 9 1 3 8 12 2 6 10 11 2 6 7 9 2 6 8 12 5 1 11 7 5 1 8 10 5 1 9 12 2 4 11 7 2 4 8 10 2 4 9 12 3 6 11 7 3 6 8 10 3 6 9 12 Weighing matrices, A generalization of Hadamard matrices that allows zero entries, are used in some combinatoric designs. In particular, the design of experiments for estimating the individual weights of multiple objects in few trials. A Youden square is a k × v rectangular array (k < v) of v symbols such that each symbol appears exactly once in each row and the symbols appearing in any column form a block of a symmetric (v, k, λ) design, all the blocks of which occur in this manner. A Youden square is a Latin rectangle. The term "square" in the name comes from an older definition which did use a square array. An example of a 4 × 7 Youden square is given by:
The seven blocks (columns) form the order 2 biplane (a symmetric (7,4,2)-design).
== See also == Algebraic statistics Hypergraph Williamson conjecture
== Notes ==
== References ==