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math.NT2026
The Normal Form of Smith's Matrices
Wenzhong Lei, Han Zhang
For any integers and , let and stand for the greatest common divisor and the least common multiple of and , respectively. We denote by the numbe…
math.NT2026
On Zeckendorf-Niven numbers and arithmetic progressions
Kelly Lao, Steven J. Miller, Nicholas Rosa +4
A positive integer is Zeckendorf-Niven (respectively, Lucas-Niven) if it is divisible by the number of summands in its Zeckendorf decomposition (respectively, Lucas decomposition).…
math.NT2023
On connectedness in the parametric geometry of numbers
Yuming Wei, Han Zhang
Via multilinear algebra, we formulate a criterion for connectedness in the parametric geometry of numbers in terms of pencils, which are certain algebraic varieties in the space of…