5 papers
Analytic Properties of Necklace Polynomials
Sunil K. Chebolu, Ján MináÄ, Tung T. Nguyen +1
The necklace polynomials \[ M_n(x)=\frac1n\sum_{d\mid n}μ(d)x^{n/d} \] play a central role in discrete mathematics: they count aperiodic necklaces, enumerate monic irreducible pol…
Maps preserving the sum-to-difference ratio
Sunil Chebolu, Apoorva Khare, Anindya Sen
For a field , what are all functions that satisfy the functional equation $f \left( (x+y)/(x-y) \right) = (f(x) + f(y))/(f(…
Maps preserving the sum-to-difference ratio in characteristic
Sunil Chebolu, Apoorva Khare, Anindya Sen
Given a field , we introduce a novel group of its self-maps: the solutions to the functional equati…
The complexities of falling freely
Anindya Sen, Sunil Chebolu
Suppose you drop a coin from 10 feet above the ground. How long does it take to reach the ground? This routine exercise is well-known to every AP physics and calculus student: the…
Rabbit Hunting using Set Theory and Probability
Sunil Chebolu, Deepayan Sarakar
Imagine an invisible rabbit that starts at some unknown integer point on the number line. At each time step, it hops by a fixed but unknown integer stride . Both and …