3 papers
math.NT2026
Gap-Sums via Quasi-Arithmetic Means with Applications to Fibonacci and Lucas Sequences
Omid Khormali, Ghaya Mtimet, Nuh Aydin +1
We develop a unified framework for studying the integers missing between consecutive terms of an increasing integer sequence, extending Barry's arithmetic gap-sum to geometric and…
math.HO2026
On the History of the Square and Multiply Algorithm
Nuh Aydin, Mohammad K. Azarian, Omid Khormali +1
The square-and-multiply algorithm, also known as binary exponentiation or repeated squaring, is a standard method for fast exponentiation in modern computation. Its historical orig…
cs.FL2026
From Historical Puzzles to Grammatical Constraints: Circular Partitions, Generalized Run-Length Encodings, and Polynomial-Time Decidability
Omid Khormali, Ghaya Mtimet, Nuh Aydin
Motivated by a historical combinatorial problem that resembles the well-known Josephus problem, we investigate circular partition algorithms and formulate problems in deterministic…