Monotonic permutations of chains

Untangled Monotonic Chains and Adaptive Range Search

We present the first adaptive data structure for two-dimensional orthogonal range search. Our data structure is adaptive in the sense that it gives improved search performance for data with more inherent sortedness. Given n points in the plane, it can answer range queries in O(k logn+m) time, where m is the number of points in the output and k is the minimum number of monotonic chains into whic...

Finite Homomorphism-Homogeneous Permutations via Edge Colourings of Chains

A relational structure is homomorphism-homogeneous if any homomorphism between its finite substructures extends to an endomorphism of the structure in question. In this note, we characterise all permutations on a finite set enjoying this property. To accomplish this, we switch from the more traditional view of a permutation as a set endowed with two linear orders to a different representation b...

Distributions of permutations generated by inhomogeneous Markov chains

Sharply $(n-2)$-transitive Sets of Permutations

Let $S_n$ be the symmetric group on the set $[n]={1, 2, ldots, n}$. For $gin S_n$ let $fix(g)$ denote the number of fixed points of $g$. A subset $S$ of $S_n$ is called $t$-emph{transitive} if for any two $t$-tuples $(x_1,x_2,ldots,x_t)$ and $(y_1,y_2,ldots ,y_t)$ of distinct elements of $[n]$, there exists $gin S$ such that $x_{i}^g=y_{i}$ for any $1leq ileq t$ and additionally $S$ is called e...

Monotonic and Dual Monotonic Language

Monotonic and dual monotonic language learning from positive as well as from positive and negative examples is investigated. Three di erent notions of monotonicity are considered. Each of them re ects an alternative formalization of the requirement that the learner has to produce better and better generalizations when fed more and more data on the concept to be learned. Strong{monotonicity abso...