Related papers: Sorting by Prefix Block-Interchanges
In genome rearrangements, the mutational event transposition swaps two adjacent blocks of genes in one chromosome. The Transposition Distance Problem (TDP) aims to find the minimum number of transpositions required to transform one…
We introduce the stack-sorting map $\text{SC}_\sigma$ that sorts, in a right-greedy manner, an input permutation through a stack that avoids some vincular pattern $\sigma$. The stack-sorting maps of Cerbai et al. in which the stack avoids a…
We address the problem of computing distances between rankings that take into account similarities between candidates. The need for evaluating such distances is governed by applications as diverse as rank aggregation, bioinformatics, social…
We continue the study of Adin, Alon and Roichman [arXiv:2502.14398, 2025] on the number of steps required to sort $n$ labelled points on a circle by transpositions. Imagine that the vertices of a cycle of length $n$ are labelled by the…
Pancake flipping, a famous open problem in computer science, can be formalised as the problem of sorting a permutation of positive integers using as few prefix reversals as possible. In that context, a prefix reversal of length k reverses…
An algorithm is presented for unranking permutations in transposition order: Given a seed s\in N, the algorithm produces a permutation P(s) that differs from the permutation P(s+1) by the transposition of two elements.
In-place associative integer sorting technique was developed, improved and specialized for distinct integers. The technique is suitable for integer sorting. Hence, given a list S of n integers S[0...n-1], the technique sorts the integers in…
We study sorting by queues that can rearrange their content by applying permutations from a predefined set. These new sorting devices are called shuffle queues and we investigate those of them corresponding to sets of permutations defining…
The Interval poset of a permutation is an effective way of capturing all the intervals of the permutation and the inclusions between them and was introduced recently by Tenner. Thi paper explores the geometric interpretation of interval…
The special purpose sorting operation, context directed swap (CDS), is an example of the block interchange sorting operation studied in prior work on permutation sorting. CDS has been postulated to model certain molecular sorting events…
We describe an algorithm, implemented in Python, which can enumerate any permutation class with polynomial enumeration from a structural description of the class. In particular, this allows us to find formulas for the number of permutations…
A problem that arises in drawings of transportation networks is to minimize the number of crossings between different transportation lines. While this can be done efficiently under specific constraints, not all solutions are visually…
Sequence models such as transformers require inputs to be represented as one-dimensional sequences. In vision, this typically involves flattening images using a fixed row-major (raster-scan) order. While full self-attention is…
There exists a bijection between one stack sortable permutations --permutations which avoid the pattern 231-- and planar trees. We define an edit distance between permutations which is coherent with the standard edit distance between trees.…
A permutation graph is the intersection graph of a set of segments between two parallel lines. In other words, they are defined by a permutation $\pi$ on $n$ elements, such that $u$ and $v$ are adjacent if an only if $u<v$ but…
Collective classification models attempt to improve classification performance by taking into account the class labels of related instances. However, they tend not to learn patterns of interactions between classes and/or make the assumption…
We extend Stanley's work on alternating permutations with extremal number of fixed points in two directions: first, alternating permutations are replaced by permutations with a prescribed descent set; second, instead of simply counting…
A permutation is called {\it {block-wise simple}} if it contains no interval of the form $p_1\oplus p_2$ or $p_1 \ominus p_2$. We present this new set of permutations and explore some of its combinatorial properties. We present a generating…
In this paper, we study the problem of sorting unichromosomal linear genomes by prefix double-cut-and-joins (or DCJs) in both the signed and the unsigned settings. Prefix DCJs cut the leftmost segment of a genome and any other segment, and…
We define a map between the set of permutations that avoid either the four patterns $3214,3241,4213,4231$ or $3124,3142,4123,4132$, and the set of Dyck prefixes. This map, when restricted to either of the two classes, turns out to be a…