Related papers: Multiset permutation generation by transpositions

We present the Insertion Transformer, an iterative, partially autoregressive model for sequence generation based on insertion operations. Unlike typical autoregressive models which rely on a fixed, often left-to-right ordering of the…

Synthetic text generation is challenging and has limited success. Recently, a new architecture, called Transformers, allow machine learning models to understand better sequential data, such as translation or summarization. BERT and GPT-2,…

A permutation is called layered if it consists of the disjoint union of substrings (layers) so that the entries decrease within each layer, and increase between the layers. We find the generating function for the number of permutations on…

Generation of graphs is a major challenge for real-world tasks that require understanding the complex nature of their non-Euclidean structures. Although diffusion models have achieved notable success in graph generation recently, they are…

Dance requires skillful composition of complex movements that follow rhythmic, tonal and timbral features of music. Formally, generating dance conditioned on a piece of music can be expressed as a problem of modelling a high-dimensional…

We compute the number of ways a given permutation can be written as a product of exactly $k$ transpositions. We express this number as a linear combination of explicit geometric sequences, with coefficients which can be computed in many…

How can we generate a permutation of the numbers $1$ through $n$ so that it is hard to guess the next element given the history so far? The twist is that the generator of the permutation (the ``Dealer") has limited memory, while the…

In this paper, we investigate the reconstruction of permutations on {1, 2, ..., n} from betweenness constraints involving the minimum and the maximum element located between t and t+1, for all t=1, 2, ..., n-1. We propose two variants of…

Permutation symmetries of multipartite quantum states are defined only when the constituent subsystems are of equal dimensions. In this work we extend this notion of permutation symmetry to heterogeneous systems, that is, systems composed…

Conditional neural text generation models generate high-quality outputs, but often concentrate around a mode when what we really want is a diverse set of options. We present a search algorithm to construct lattices encoding a massive number…

In this paper, we propose a method to build molecular cages designed to capture a specific substrate. We model a cage as a graph of atoms with coordinates in space, and several constraints on their edges (degree, length and angle). We use a…

We present a method for storing multiple models within a single set of parameters. Models can coexist in superposition and still be retrieved individually. In experiments with neural networks, we show that a surprisingly large number of…

We prove a lower and an upper bound on the number of block moves necessary to sort a permutation. We put our results in contrast with existing results on sorting by block transpositions, and raise some open questions.

We apply ideas from the cluster method to q-count the permutations of a multiset according to the number of occurrences of certain generalized patterns, as defined by Babson and Steingrimsson. In particular, we consider those patterns with…

We establish that any even permutation from A_n moving at least [3n/4] + o(n) points is the commutator of a generating pair of A_n and a generating pair of S_n. From this we deduce an exponential lower bound on the number of systems of…

This article focuses on automatically generating polynomial equations that are inductive loop invariants of computer programs. We propose a new algorithm for this task, which is based on polynomial interpolation. Though the proposed…

Compression aims to reduce the size of an input, while maintaining its relevant properties. For multi-parameter persistent homology, compression is a necessary step in any computational pipeline, since standard constructions lead to large…

Evolutionary algorithms usually explore a search space of solutions by means of crossover and mutation. While a mutation consists of a small, local modification of a solution, crossover mixes the genetic information of two solutions to…

Motivated by charge balancing constraints for rank modulation schemes, we introduce the notion of balanced permutations and derive the capacity of balanced permutation codes. We also describe simple interleaving methods for permutation code…

Hypergraphs are used to model higher-order interactions amongst agents and there exist many practically relevant instances of hypergraph datasets. To enable efficient processing of hypergraph-structured data, several hypergraph neural…