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Results tagged with combinatorial-designs
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user 9025
Design theory is the subfield of combinatorics concerning the existence and construction of highly symmetric arrangements. Finite projective planes, latin squares, and Steiner triple systems are examples of designs.
2
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Accepted
Reference Request: "Resolutions" of $K_n$ for $n$ odd
I might be missing something, but it looks like you want a partition of the edges of $K_n$, odd $n$, into a set of subgraphs which are regular of degree 2. That's called a 2-factorization. It can be …
- 37.7k
7
votes
Latin squares with one cycle type?
There are also "pan-Hamiltonian" Latin squares, see Perfect Factorisations of Bipartite Graphs and Latin Squares Without Proper Subrectangles by I. M. Wanless, Electronic J. Combin. 6 (1999), R9.
- 37.7k
4
votes
Accepted
Isomorphism testing in STS(13)
Take the 26-vertex graphs whose vertices are the blocks and where two vertices are joined by an edge if the corresponding blocks have a vertex in common. These two graphs differ in many easily measur …
- 37.7k
2
votes
For which sets of $(n, m, k)$ does there exist an edge-labelling (using $k$ labels) on $K_n$...
This is a standard problem in design theory. A Steiner system $S(t, k, v)$ is a pair $(X, B)$, where $X$ is a $v$-element set and $B$ is a set of $k$-subsets of $X$, called blocks, with the property …
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