Related papers: Multiset permutation generation by transpositions

In this paper we present a novel algorithm for computing a congruence on an inverse semigroup from a collection of generating pairs. This algorithm uses a myriad of techniques from the theories of groups, automata, and inverse semigroups.…

To constitute atoms of a $\sigma$ algebra is not a easy task due to the large number of its elements. However, determining them via generators seems a feasible and simple way since most $\sigma$ algebras are generated by their smaller…

Discrete mixture models provide a well-known basis for effective clustering algorithms, although technical challenges have limited their scope. In the context of gene-expression data analysis, a model is presented that mixes over a finite…

The so-called permutation separability criteria are simple operational conditions that are necessary for separability of mixed states of multipartite systems: (1) permute the indices of the density matrix and (2) check if the trace norm of…

In this paper, we introduce a convergence notion for ordered selections. Our convergence notion is based on subpermutation densities and convergences of the marginal distributions. A particular case of this convergence is the well-known…

Data for pretraining machine learning models often consists of collections of heterogeneous datasets. Although training on their union is reasonable in agnostic settings, it might be suboptimal when the target domain -- where the model will…

In the context of the genome rearrangement problem, we analyze two well known models, namely the block transposition and the prefix block transposition models, by exploiting the connection with the notion of permutation pattern. More…

Let $S_n$ denote the group all permutations of $n$. For every permutation $\sigma$, we let $\mathrm{des}(\sigma)$ denote the number of descents in $\sigma$ and $\mathrm{LRMin}(\sigma)$ denote the number of left-to-right minima of $\sigma$.…

Machines whose main purpose is to permute and sort data are studied. The sets of permutations that can arise are analysed by means of finite automata and avoided pattern techniques. Conditions are given for these sets being enumerated by…

This paper introduces a deterministic algorithm for solving an instance of the Subset Sum Problem based on a new method entitled the Bipartite Synthesis Method. The algorithm is described and shown to have worst-case limiting performance…

The generation of random graphs using edge swaps provides a reliable method to draw uniformly random samples of sets of graphs respecting some simple constraints, e.g. degree distributions. However, in general, it is not necessarily…

We propose Composition Sampling, a simple but effective method to generate diverse outputs for conditional generation of higher quality compared to previous stochastic decoding strategies. It builds on recently proposed plan-based neural…

Permutation polynomials and their compositional inverses have wide applications in cryptography, coding theory, and combinatorial designs. Motivated by several previous results on finding compositional inverses of permutation polynomials of…

In this paper we give a fast algorithm to generate all partitions of a positive integer $n$. Integer partitions may be encoded as either ascending or descending compositions for the purposes of systematic generation. It is known that the…

To generate new images for a given category, most deep generative models require abundant training images from this category, which are often too expensive to acquire. To achieve the goal of generation based on only a few images, we propose…

A method of fast linear transform algorithm synthesis for an arbitrary tensor, matrix, or vector is proposed. The method is based on factorization of a tensor and using the factors for building computational structures performing fast…

It is a classical problem to compute a minimal set of invariant polynomial generating the invariant ring of a finite group as an algebra. We present here an algorithm for the computation of minimal generating sets in the non-modular case.…

In comparative genomics, a transposition is an operation that exchanges two consecutive sequences of genes in a genome. The transposition distance, that is, the minimum number of transpositions needed to transform a genome into another, is,…

This note proposes a simple and general framework of dynamic mode decomposition (DMD) and a mode selection for large datasets. The proposed framework explicitly introduces a preconditioning step using an incremental proper orthogonal…

Permutations are usually enumerated by size, but new results can be found by enumerating them by inversions instead, in which case one must restrict one's attention to indecomposable permutations. In the style of the seminal paper by Simion…