Related papers: Chinese Names for Integers
Multiplication and exponentiation can be defined by equations in which one of the operands is written as the sum of powers of two. When these powers are non-negative integers, the operand is integer; without this restriction it is a…
Revisiting a $50$-year-old estimate of Choi, Erd\H{o}s and Szemer\'edi, we show that if $A \subseteq \{1, 2, \ldots, 2n\}$ satisfies $|A| \ge n + 1.2 \cdot 10^8$, then there exist five distinct integers whose pairwise sums are all contained…
The mathematical constant pi has recently been computed up to 22,459,157,718,361 decimal and 18,651,926,753,033 hexadecimal digits. As a simple check for the normality of pi, the frequencies of all sequences with length one, two and three…
Chinese couplet is a special form of poetry composed of complex syntax with ancient Chinese language. Due to the complexity of semantic and grammatical rules, creation of a suitable couplet is a formidable challenge. This paper presents a…
We consider numeration systems with base $\beta$ and $-\beta$, for quadratic Pisot numbers $\beta$ and focus on comparing the combinatorial structure of the sets $\Z_\beta$ and $\Z_{-\beta}$ of numbers with integer expansion in base…
When sharing or logging numerical data, we must convert binary floating-point numbers into their decimal string representations. For example, the number $\pi$ might become 3.1415927. Engineers have perfected many algorithms for producing…
A classic question in analytic number theory is to find asymptotics for $\sigma_{k}(x)$ and $\pi_{k}(x)$, the number of integers $n\leq x$ with exactly $k$ prime factors, where $\pi_{k}(x)$ has the added constraint that all the factors are…
Cryptography, derived from Greek meaning hidden writing, uses mathematical techniques to secure information by converting it into an unreadable format. While cryptography as a science began around 100 years ago, its roots trace back to…
Tao has shown that in any fixed base, a positive proportion of prime numbers cannot have any digit changed and remain prime. In other words, most primes are "digitally delicate". We strengthen this result in a manner suggested by Tao: A…
We construct a finite convergent semi-quadratic presentation for the Chinese monoid by adding column generators and using combinatorial properties of insertion algorithms on Chinese staircases. We extend this presentation into a coherent…
Sumterms are introduced as syntactic entities, and sumtuples are introduced as semantic entities. Equipped with these concepts a new description is obtained of the notion of a sum as (the name for) a role which can be played by a number.…
Chinese calligraphy is the writing of Chinese characters as an art form performed with brushes so Chinese characters are rich of shapes and details. Recent studies show that Chinese characters can be generated through image-to-image…
To automatically correct handwritten assignments, the traditional approach is to use an OCR model to recognize characters and compare them to answers. The OCR model easily gets confused on recognizing handwritten Chinese characters, and the…
We extend our previous results on the number of integers which are values of some cyclotomic form of degree larger than a given value (see \cite{FW1}), to more general families of binary forms with integer coefficients. Our main ingredient…
Constructing historical language models (LMs) plays a crucial role in aiding archaeological provenance studies and understanding ancient cultures. However, existing resources present major challenges for training effective LMs on historical…
We empirically study the genealogical trees of ten families for about five centuries in Korea. Although each family tree contains only the paternal part, the family names of women married to the family have been recorded, which allows us to…
Chinese character recognition has attracted much research interest due to its wide applications. Although it has been studied for many years, some issues in this field have not been completely resolved yet, e.g. the zero-shot problem.…
For relatively prime positive integers u_0 and r, we consider the arithmetic progression {u_k := u_0+k*r} (0 <= k <= n). Define L_n := lcm{u_0,u_1,...,u_n} and let a >= 2 be any integer. In this paper, we show that, for integers alpha,r >=…
Designing fonts for Chinese characters is highly labor-intensive and time-consuming. While the latest methods successfully generate the English alphabet vector font, despite the high demand for automatic font generation, Chinese vector font…
Given a countable set X (usually taken to be the natural numbers or integers), an infinite permutation, \pi, of X is a linear ordering of X. This paper investigates the combinatorial complexity of infinite permutations on the natural…