๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

The three-permutations problem

โœ Scribed by P.C. Fishburn; W.V. Gehrlein

Book ID
103056197
Publisher
Elsevier Science
Year
1990
Tongue
English
Weight
332 KB
Volume
79
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

โœฆ Synopsis

Given any three permutations on { 1, . . , n}, we want to choose f : { 1, . . . , n} + { -1, 1) so that the maximum absolute partial sum off values over the permutations is minimized. The three-permutations problem is to determine the supremum of this minimum taken over all n and all triples of permutations on {l, , n}. The only thing presently known about the supremum is that it is at least two. This paper establishes a result for a restricted case of the problem in which the maximum absolute partial sum for one of the three permutations equals 1. The supremum in this case is unbounded.

๐Ÿ“œ SIMILAR VOLUMES

A problem with permutations, I
A problem with permutations, I
โœ E.T Parker; Gerald A Dyer ๐Ÿ“‚ Article ๐Ÿ“… 1979 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 73 KB
Some permutation problems
Some permutation problems
โœ L Carlitz; Richard Scoville ๐Ÿ“‚ Article ๐Ÿ“… 1977 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 588 KB
On the matrix permutation problem
On the matrix permutation problem
โœ M. Tegze; M. Vlach ๐Ÿ“‚ Article ๐Ÿ“… 1986 ๐Ÿ› Springer ๐ŸŒ English โš– 220 KB
A Problem in Permutations: the Game of '
A Problem in Permutations: the Game of 'Mousetrap'
โœ Daniel J. Mundfrom ๐Ÿ“‚ Article ๐Ÿ“… 1994 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 190 KB

The game of 'Mousetrap, a problem in permutations, first introduced by Arthur Cayley in 1857 and independently addressed by Cayley and Adolph Steen in 1878, has been largely unexamined since. The game involves permutations of \(n\) cards numbered consecutively from 1 to \(n\). The cards are laid out