Arithmetic properties of powers of Gaussian polynomials

Term: 
2024-2025 Spring
Faculty Department of Project Supervisor: 
Faculty of Engineering and Natural Sciences
Number of Students: 
4

Everyone knows the binomial coefficients "n choose k" = n! / ( k! (n-k)! ) for 0 <= k <= n . If we replace each integer r by the polynomial 1 + q + q^2 + ... + q^{r-1} in the fomula, we obtain Gaussian polynomials, or q-binomial coefficients.  With the help of computers, the students will search patterns among coefficients of Gaussian polynomials, and their powers.  The more eager students will learn about cylindric partitions, and put their findings into use in that context.  The even more eager student will learn about q-series, and try to prove any empirical result. 

Related Areas of Project: 
Computer Science and Engineering
​Mathematics

About Project Supervisors

supersivor: Kağan Kurşungöz
webpage: https://people.sabanciuniv.edu/~kursungoz/
e-mail: kursungoz@sabanciuniv.edu