Related papers: Chinese Names for Integers

The problem of determining cyclotomic numbers in terms of the solutions of certain Diophantine systems has been treated by many authors since the age of Gauss. In this paper we obtain an explicit expression for cyclotomic numbers of order…

The hierarchy of classical Chinese poetry has been broadly acknowledged by a number of studies in Chinese literature. However, quantitative investigations about the evolutionary linkages of classical Chinese poetry are limited. The primary…

While recent work has begun to uncover the internal strategies that Large Language Models (LLMs) employ for simple arithmetic tasks, a unified understanding of their underlying mechanisms is still lacking. We extend recent findings showing…

We introduce \emph{patterned numbers}, a digit--divisor-based classification of integers motivated by recreational mathematics. A number is defined to be patterned if at least one of its positive divisors appears as a digit in its base-10…

An algorithm is given to factor an integer with $N$ digits in $\ln^m N$ steps, with $m$ approximately 4 or 5. Textbook quadratic sieve methods are exponentially slower. An improvement with the aid of an a particular function would provide a…

We systematically investigate geometric patterns in Chinese character embeddings using PHATE manifold analysis. Through cross-validation across seven embedding models and eight dimensionality reduction methods, we observe clustering…

We describe a method of using statistically-collected Chinese character groups from a corpus to augment a Chinese dictionary. The method is particularly useful for extracting domain-specific and regional words not readily available in…

Handwriting of Chinese has long been an important skill in East Asia. However, automatic generation of handwritten Chinese characters poses a great challenge due to the large number of characters. Various machine learning techniques have…

A permutation of the integers avoiding monotone arithmetic progressions of length $6$ was constructed in (Geneson, 2018). We improve on this by constructing a permutation of the integers avoiding monotone arithmetic progressions of length…

This paper aimed to provide an approach to investigate the historical roots and evolution of research fields in China by extending the reference publication year spectroscopy (RPYS). RootCite, an open source software accepts raw data from…

A permutiple is the product of a digit preserving multiplication, that is, a number which is an integer multiple of some permutation of its digits. Certain permutiple problems, particularly transposable, cyclic, and, more recently,…

Let $f$ be a fixed (holomorphic or Maass) modular cusp form. Let $\cq$ be a Dirichlet character mod $q$. We describe a fast algorithm that computes the value $L(1/2,f\times\chi_q)$ up to any specified precision. In the case when $q$ is…

Whole word masking (WWM), which masks all subwords corresponding to a word at once, makes a better English BERT model. For the Chinese language, however, there is no subword because each token is an atomic character. The meaning of a word…

Given a base $b$, a "digit map" is a map $f: \mathbb{Z}^{\ge 0} \to \mathbb{Z}^{\ge 0}$ of the form $f(\sum_{i=0}^n a_ib^i) = \sum_{i=0}^n f_*(a_i)$, $0 \le a_i \le b-1$ for each $i$, where $f_* : \{0,1,\dots, b-1\} \to \mathbb{Z}^{\ge 0}$…

Taxonomies play an important role in machine intelligence. However, most well-known taxonomies are in English, and non-English taxonomies, especially Chinese ones, are still very rare. In this paper, we focus on automatic Chinese taxonomy…

Multisets are like sets, except that they can contain multiple copies of their elements. If there are $n_i$ copies of $i$, $1\leq i\leq t$, in multiset $M_t$, then there are $\binom{n_1+\cdots+n_t}{n_1,\ldots, n_t}$ possible permutations of…

In this note, we present a new proof that the cyclotomic integers constitute the full ring of integers in the cyclotomic field.

There have been many theories about the paradoxes of numbers, but this is far and away more paradoxical than most. In this paper we will present the Zoli Numbers which have some innovative characteristics. The basic concept of these numbers…

Linguistics holds unique characteristics of generality, stability, and nationality, which will affect the formulation of extraction strategies and should be incorporated into the relation extraction. Chinese open relation extraction is not…

First we reprove two results in additive number theory due to Dombi and Chen & Wang, respectively, on the number of representations of n as the sum of two odious or evil numbers, using techniques from automata theory and logic. We also use…