SeminYoo

$q$-analogues of quantities in mathematics involve perturbations of classical quantities using the parameter $q$, and revert to the original quantities when $q$ goes $1$. An important example is the $q$-analogues of binomial coefficients, denoted by ${(\genfrac{}{}{0ex}{}{n}{k})}_q$, which give the number of $k$-dimensional subspaces in ${\mathbb{F}}_q^n$. When $q$ goes to $1$, this reverts to the binomial …

We provide new constructions of families of quasi-random graphs that behave like Paley graphs but are neither Cayley graphs nor Cayley sum graphs. These graphs give a unified perspective of studying various graphs defined by polynomials over finite fields, such as Paley graphs, Paley sum graphs, and graphs associated with Diophantine tuples and their generalizations …