The Maximal Length of a $k$-Separator Permutation

The Maximal Length of a k-Separator Permutation

A permutation σ ∈ Sn is a k-separator if all of its patterns of length k are distinct. Let F (k) denote the maximal length of a k-separator. Hegarty (2013) showed that k + ⌊√ 2k − 1 ⌋ − 1 6 F (k) 6 k + ⌊√ 2k − 3 ⌋ , and conjectured that F (k) = k + ⌊√ 2k − 1 ⌋ − 1. This paper will strengthen the upper bound to prove the conjecture for all sufficiently large k (in particular, for all k > 320801).

On the Maximal Degree of the K-Step Obrechkoff’s Method

Preserving the Number of Cycles of Length k in a Growing Uniform Permutation

The goal of this work is to describe a uniform generation tree for permutations which preserves the number of k-cycles between any permutation (except for a small unavoidable subset of optimal size) of the tree and its direct children. Moreover, the tree we describe has the property that if the number of k-cycles does not change during any k consecutive levels, then any further random descent w...

determination of maximal singularity free zones in the workspace of parallel manipulator

due to the limiting workspace of parallel manipulator and regarding to finding the trajectory planning of singularity free at workspace is difficult, so finding a best solution that can develop a technique to determine the singularity-free zones in the workspace of parallel manipulators is highly important. in this thesis a simple and new technique are presented to determine the maximal singula...

On Maximal Equidistant Permutation Arrays

An equidistant permutation array A(r, I ; u ) is a t' x r array defined on a symbol set V such that each row of the array is a permutation of the symbol set V and any two distinct rows of A have precisely A common column entries. Given r and i.. one can ask for the largest u such that an A(r, 2.; v) exists or find the smallest v such that an A(r, I; u ) exists which cannot be extended to an A(r...