Related papers: On Bijective Variants of the Burrows-Wheeler Trans…

Generalizing stack sorting and $c$-sorting for permutations, we define the permutree sorting algorithm. Given two disjoint subsets $U$ and $D$ of $\{2, \dots, n-1\}$, the $(U,D)$-permutree sorting tries to sort the permutation $\pi \in…

The coinvariant algebra is a quotient of the polynomial ring $\mathbb{Q}[x_1,\ldots,x_n]$ whose algebraic properties are governed by the combinatorics of permutations of length $n$. A word $w = w_1 \dots w_n$ over the positive integers is…

We exhibit a bijection between recently-introduced combinatorial objects known as valid hook configurations and certain weighted set partitions. When restricting our attention to set partitions that are matchings, we obtain three new…

For positive integers $k,n$, a de Bruijn sequence $B(k,n)$ is a finite sequence of elements drawn from $k$ characters whose subwords of length $n$ are exactly the $k^n$ words of length $n$ on $k$ characters. This paper introduces the…

Let $w$ be a word in alphabet $\{x,D\}$ with $m$ $x$'s and $n$ $D$'s. Interpreting "$x$" as multiplication by $x$, and "$D$" as differentiation with respect to $x$, the identity $wf(x) = x^{m-n}\sum_k S_w(k) x^k D^k f(x)$, valid for any…

We initiate the study of sorting permutations using prefix block-interchanges, which exchange any prefix of a permutation with another non-intersecting interval. The goal is to transform a given permutation into the identity permutation…

We study the sequence-to-sequence mapping capacity of transformers by relating them to finite transducers, and find that they can express surprisingly large classes of transductions. We do so using variants of RASP, a programming language…

We propose a novel transformer-based styled handwritten text image generation approach, HWT, that strives to learn both style-content entanglement as well as global and local writing style patterns. The proposed HWT captures the long and…

We extend and generalize many of the enumerative results concerning West's stack-sorting map $s$. First, we prove a useful theorem that allows one to efficiently compute $|s^{-1}(\pi)|$ for any permutation $\pi$, answering a question of…

This paper presents the Bayesian Hierarchical Words Representation (BHWR) learning algorithm. BHWR facilitates Variational Bayes word representation learning combined with semantic taxonomy modeling via hierarchical priors. By propagating…

A finite Sturmian word w over the alphabet {a,b} is left special (resp. right special) if aw and bw (resp. wa and wb) are both Sturmian words. A bispecial Sturmian word is a Sturmian word that is both left and right special. We show as a…

We consider the number of passes a permutation needs to take through a stack if we only pop the appropriate output values and start over with the remaining entries in their original order. We define a permutation $\pi$ to be $k$-pass…

In machine translation (MT) that involves translating between two languages with significant differences in word order, determining the correct word order of translated words is a major challenge. The dependency parse tree of a source…

Consider an input text string T[1,N] drawn from an unbounded alphabet. We study partial computation in suffix-based problems for Data Compression and Text Indexing such as (I) retrieve any segment of K<=N consecutive symbols from the…

We present an equivariant bijection between two actions--promotion and rowmotion--on order ideals in certain posets. This bijection simultaneously generalizes a result of R. Stanley concerning promotion on the linear extensions of two…

Word reordering is one of the most difficult aspects of statistical machine translation (SMT), and an important factor of its quality and efficiency. Despite the vast amount of research published to date, the interest of the community in…

There is a natural bijection between permutations obtainable using a stack (those avoiding the pattern 312) and permutations obtainable using a queue (those avoiding 321). This bijection is equivalent to one described by Simion and Schmidt…

In-place associative integer sorting technique was proposed for integer lists which requires only constant amount of additional memory replacing bucket sort, distribution counting sort and address calculation sort family of algorithms. The…

Though early successes of Statistical Machine Translation (SMT) systems are attributed in part to the explicit modelling of the interaction between any two source and target units, e.g., alignment, the recent Neural Machine Translation…

We consider symbolic tree automata (sta) and symbolic tree transducers (stt). We characterize s-recognizable tree languages (which are the tree languages recognizable by sta) in terms of (classical) recognizable tree languages and…