Related papers: The Number System of the Old European Script
The notion of a two-dimensional word arises naturally in the study of combinatorics on words, while the iterative construction of pedal triangles results in a rich dynamical system in the study of geometry. At first, these two classes of…
Exactly 500 years ago, Nicolaus Copernicus drew a lattice of lines on a panel above the doorway to his rooms at Olsztyn Castle, then in the Bishopric of Warmia. Although its design has long been regarded as some kind of reflecting vertical…
Translated from the Latin original, "De numeris amicabilibus" (1747). E100 in the Enestroem index. Euler starts by saying that with the success of mathematical analysis, number theory has been neglected. He argues that number theory is…
This paper presents an investigation of the entropy of the Telugu script. Since this script is syllabic, and not alphabetic, the computation of entropy is somewhat complicated.
Oracle bone inscriptions(OBI) is the earliest developed writing system in China, bearing invaluable written exemplifications of early Shang history and paleography. However, the task of deciphering OBI, in the current climate of the…
Formal languages are sets of strings of symbols described by a set of rules specific to them. In this note, we discuss a certain class of formal languages, called regular languages, and put forward some elementary results. The properties of…
We give a new simple and short ("one-line") analysis for the runtime of the well-known Euclidean Algorithm. While very short simple, the obtained upper bound in near-optimal.
Recent embedding-based methods in unsupervised bilingual lexicon induction have shown good results, but generally have not leveraged orthographic (spelling) information, which can be helpful for pairs of related languages. This work…
When people mention the number theoretical achievements in Ancient China, the famous Chinese Remainder Theorem always springs to mind. But, two more of them--the concept of primes and the algorithm for counting the greatest common divisor,…
Communication plays a vital role in human interaction. Studying language is a worthwhile task and more recently has become quantitative in nature with developments of fields like quantitative comparative linguistics and lexicostatistics.…
The ancient priest-astronomers constantly watched many heavenly bodies. The record about Halley's Comet of 1682 A.D. has been decoded completely. Good agreement between it and the results of European astronomers is seen. The records about…
Writing is a universal cultural technology that reuses vision for symbolic communication. Humans display striking resilience: we readily recognize words even when characters are fragmented, fused, or partially occluded. This paper…
The Countdown game is one of the oldest TV show running in the world. It started broadcasting in 1972 on the french television and in 1982 on British channel 4, and it has been running since in both countries. The game, while extremely…
The Eulerian numbers form a triangular array with many interesting properties. The numbers arise from various combinatorial and probabilistic interpretations, and have been studied in a variety of mathematical contexts. In this article we…
The earliest origins of mathematics in the Indian subcontinent is generally dated around 800-500 BCE when the {\em Sulbasutras} are thought to have been written. In this article we suggest that mathematical thinking in South Asia, in…
The ancient and extinct language Meroitic is investigated using Zipf's Law. In particular, since Meroitic is still undeciphered, the Zipf law analysis allows us to assess the quality of current texts and possible avenues for future…
Back in 1755, Euler explored an interesting array of numbers that now frequently appears in polynomial identities, combinatorial problems, and finite calculus, among other places. These numbers share a strong connection with well-known…
Now a day computer is necessary for human being and it is very useful in many fields like search engine, text processing, short messaging services, voice chatting and text recognition. Since last many years there are many tools and…
This paper describes a system prepared at Brno University of Technology for ICDAR 2021 Competition on Historical Document Classification, experiments leading to its design, and the main findings. The solved tasks include script and font…
Across languages, numeral systems vary widely in how they construct and combine numbers. While humans consistently learn to navigate this diversity, large language models (LLMs) struggle with linguistic-mathematical puzzles involving…