相关论文: Pattern avoiding permutations are context-sensitiv…

In this paper we prove that among the permutations of length n with i fixed points and j excedances, the number of 321-avoiding ones equals the number of 132-avoiding ones, for all given i,j<=n. We use a new technique involving diagonals of…

This paper completes a project to enumerate permutations avoiding a triple T of 4-letter patterns, in the sense of classical pattern avoidance, for every T. There are 317 symmetry classes of such triples T and previous papers have…

This paper addresses the issue of implicit stereotypes that may arise during the generation process of large language models. It proposes an interpretable bias detection method aimed at identifying hidden social biases in model outputs,…

We consider the task of learning a context-dependent mapping from utterances to denotations. With only denotations at training time, we must search over a combinatorially large space of logical forms, which is even larger with…

Model interpretability methods are often used to explain NLP model decisions on tasks such as text classification, where the output space is relatively small. However, when applied to language generation, where the output space often…

A permutation is called Grassmannian if it has at most one descent. In this paper, we investigate pattern avoidance and parity restrictions for such permutations. As our main result, we derive formulas for the enumeration of Grassmannian…

We prove a conjecture of J.-C. Novelli, J.-Y. Thibon, and L. K. Williams (2010) about an equivalence of two triples of statistics on permutations. To prove this conjecture, we construct a bijection through different combinatorial objects,…

Theorems relating permutations with objects in other fields of mathematics are often stated in terms of avoided patterns. Examples include various classes of Schubert varieties from algebraic geometry (Billey and Abe 2013), commuting…

Session types describe the structure of communications implemented by channels. In particular, they prescribe the sequence of communications, whether they are input or output actions, and the type of value exchanged. Crucial to any language…

We consider the monomial expansion of the $q$-Whittaker and modified Hall-Littlewood polynomialsarising from specialization of the modified Macdonald polynomial. The two combinatorial formulas for the latter due to Haglund, Haiman, and…

In this paper, we study pattern avoidance for stabilized-interval-free (SIF) permutations. These permutations are contained in the set of indecomposable permutations and in the set of derangements. We enumerate pattern-avoiding SIF…

We consider pattern containment and avoidance with a very tight definition that was used first by Riordan more than 60 years ago. Using this definition, we prove the monotone pattern is easier to avoid than almost any other pattern of the…

Pronoun disambiguation in understanding text and discourse often requires the application of both general pragmatic knowledge and context-specific information. In AI and linguistics research, this has mostly been studied in cases where the…

We introduce a notion of contextuality for transformations in sequential contexts, distinct from the Bell-Kochen-Specker and Spekkens notions of contextuality. Within a transformation-based model for quantum computation we show that strong…

The task of obfuscating writing style using sequence models has previously been investigated under the framework of obfuscation-by-transfer, where the input text is explicitly rewritten in another style. These approaches also often lead to…

In [Kit1] Kitaev discussed simultaneous avoidance of two 3-patterns with no internal dashes, that is, where the patterns correspond to contiguous subwords in a permutation. In three essentially different cases, the numbers of such…

We investigate pattern-avoiding (0,1)-matrices as generalizations of pattern-avoiding permutations. Our emphasis is on 123-avoiding and 321-avoiding patterns for which we obtain exact results as to the maximum number of 1's such matrices…

The research on indexing repetitive string collections has focused on the same search problems used for regular string collections, though they can make little sense in this scenario. For example, the basic pattern matching query "list all…

In this paper, we consider pattern avoidance in a subset of words on $\{1,1,2,2,\dots,n,n\}$ called reverse double lists. In particular a reverse double list is a word formed by concatenating a permutation with its reversal. We enumerate…

Self-attention is a useful mechanism to build generative models for language and images. It determines the importance of context elements by comparing each element to the current time step. In this paper, we show that a very lightweight…