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Geometric sets of permutations

✍ Scribed by Peter J. Cameron


Publisher
Springer
Year
1988
Tongue
English
Weight
487 KB
Volume
25
Category
Article
ISSN
0046-5755

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πŸ“œ SIMILAR VOLUMES


Geometric permutations for convex sets
✍ M Katchalski; T Lewis; J Zaks πŸ“‚ Article πŸ“… 1985 πŸ› Elsevier Science 🌐 English βš– 657 KB
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The object of this paper is to study how many essentially different common transversals a family of convex sets on the plane can have. In particular we consider the case where the family consists of pairwise disjoint translates of a single convex set.

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Machines whose main purpose is to permute and sort data are studied. The sets of permutations that can arise are analysed by means of ΓΏnite automata and avoided pattern techniques. Conditions are given for these sets to be enumerated by rational generating functions. As a consequence we give the ΓΏrs

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On the set of n2+ n + 1 points of a projective plane, a set of ta2 + n -I-1 permutations is constructed with the property that any two are a Hamming distance 2n + 1 apart. Another set is constructed in which every pak are a Hamming distance not greater than 2n + 1 apart. Both sets are maximal with r

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If U and V are distinct points of a projective plane and I is a line not through U or V, then to each/, there corresponds a unique mapping, 2, of the pencil of lines through U onto the pencil through V such that for any line u, U su, u c~ u2 eL if a set R is used to label the lines through U, and th