Related papers: Generating function for Naturalized Series: The ca…
We investigate the coefficients generated by expressing the falling factorial $(xy)_k$ as a linear combination of falling factorial products $(x)_l (y)_m$ for $l,m =1,...,k$. Algebraic and combinatoric properties of these coefficients are…
Recently, Kitaev [Ki2] introduced partially ordered generalized patterns (POGPs) in the symmetric group, which further generalize the generalized permutation patterns introduced by Babson and Steingr\'imsson [BS]. A POGP p is a GP some of…
We consider a generating function of the domino tilings of an Aztec rectangle with several boundary unit squares removed. Our generating function involves two statistics: the rank of the tiling and half number of vertical dominoes as in the…
Recently, commonsense reasoning in text generation has attracted much attention. Generative commonsense reasoning is the task that requires machines, given a group of keywords, to compose a single coherent sentence with commonsense…
Let $c_n$ denote the number of nodes at a distance $n$ from the root of a rooted tree. A criterion for proving the rationality and computing the rational generating function of the sequence $\{c_n\}$ is described. This criterion is applied…
For every finitely generated free group we construct an explicit left order extending the lexicographic order on the free monoid generated by the positive letters. The order is defined by a left, free action on the orbit of 0 of a free…
In this paper, we introduce a novel natural language generation task, termed as text morphing, which targets at generating the intermediate sentences that are fluency and smooth with the two input sentences. We propose the Morphing Networks…
Text generation is a fundamental building block in natural language processing tasks. Existing sequential models performs autoregression directly over the text sequence and have difficulty generating long sentences of complex structures.…
Recent advances in large pre-trained language models have demonstrated strong results in generating natural languages and significantly improved performances for many natural language generation (NLG) applications such as machine…
Current storytelling systems focus more ongenerating stories with coherent plots regard-less of the narration style, which is impor-tant for controllable text generation. There-fore, we propose a new task, stylized story gen-eration, namely…
We present an algorithm which, for given $n$, generates an unambiguous regular tree grammar defining the set of combinatory logic terms, over the set $\{S,K\}$ of primitive combinators, requiring exactly $n$ normal-order reduction steps to…
Recent language models, especially those based on recurrent neural networks (RNNs), make it possible to generate natural language from a learned probability. Language generation has wide applications including machine translation,…
The aim of this note is to survey the factorizations of the Fibonacci infinite word that make use of the Fibonacci words and other related words, and to show that all these factorizations can be easily derived in sequence starting from…
Distributed representations of words have boosted the performance of many Natural Language Processing tasks. However, usually only one representation per word is obtained, not acknowledging the fact that some words have multiple meanings.…
We obtain an index of the complexity of a random sequence by allowing the role of the measure in classical probability theory to be played by a function we call the generating mechanism. Typically, this generating mechanism will be a finite…
The idea of generating integrals analogous to generating functions is first introduced in this paper. A new proof of the well-known Finite Harmonic Series Theorem in Analysis and Analytical Number Theory is then obtained by the method of…
Sentence function is an important linguistic feature indicating the communicative purpose in uttering a sentence. Incorporating sentence functions into conversations has shown improvements in the quality of generated responses. However, the…
We find the generating function for $C(n,k,r)$, the number of compositions of $n$ into $k$ positive parts all of whose runs (contiguous blocks of constant parts) have lengths less than $r$, using recent generalizations of the method of…
Incorporating prior knowledge like lexical constraints into the model's output to generate meaningful and coherent sentences has many applications in dialogue system, machine translation, image captioning, etc. However, existing RNN-based…
Word embedding is a powerful tool in natural language processing. In this paper we consider the problem of word embedding composition \--- given vector representations of two words, compute a vector for the entire phrase. We give a…