# Concerning a certain set of arrangements

@inproceedings{Dushnik1950ConcerningAC, title={Concerning a certain set of arrangements}, author={Ben Dushnik}, year={1950} }

there exists an arrangement in S in which ak follows all the a, with i < k. Such sets S surely exist; for example, any set of m arrangements whose terminal elements are 1, 2, , m, respectively, will obviously be k-suitable for any k ? m. The smallest cardinal number N such that there exists a set of N arrangements which is k-suitable for m will be denoted by N(m, k); this is therefore a well defined positive integer for any m and k, k <m. In any collection of arrangements of the first m…

## 65 Citations

On the Order Dimension of 1-Sets versus k-Sets

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Pairwise Suitable Family of Permutations and Boxicity

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A family F of permutations of the vertices of a hypergraph H is called "pairwise suitable" for H if, for every pair of disjoint edges in H, there exists a permutation in F in which all the vertices…

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Minimal scrambling sets of simple orders

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Abstract : Let 2 < or = k < n be fixed integers, a family F of simple orders on an n element set is said to be k-suitable if of every k elements in the n set, each one is the largest of the k in some…

The dimension of interior levels of the Boolean lattice

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AbstractLetP(k,r;n) denote the containment order generated by thek-element andr-element subsets of ann-element set, and letd(k,r;n) be its dimension. Previous research in this area has focused on the…

On the λ-Dimension and the A-Dimension of Partially Ordered Sets

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Let S be an abstract set and K a collection of linear orders defined on S. Define a partial order P on S as follows. For any two elements p and q in S put p < q in P if and only if p < q for each…

Three Problems Involving Permutations

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- 2016

We study three problems involving permutations: the n-card problem, inv-Wilf-equivalence, and suitable sets of permutations. The n-card problem is to determine the minimal intervals [u, v] such that…

Sequence Covering Arrays and Linear Extensions

- Mathematics, Computer ScienceIWOCA
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A post-optimization method to make a permutation redundant so that it can be removed and the set size reduced is developed, and preliminary results on sequence covering arrays show that it is surprisingly effective.

## References

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