# Combinatorics Seminar

Combinatorics of quadratic spaces over finite fields

Semin Yoo, (U of R)

4:00 PM - 5:00 PM

Zoom id 573 239 4086

In this talk, I will talk about the combinatorial structures associated with quadratic spaces over finite fields. I will first introduce a new isometric invariant of combinatorial type in $(\mathbb{F}*{q}^{n},x*{1}^{2}+x_{2}^{2}+\cdots+x_{n}^{2})$, where $q$ is an odd prime power. Using counts from this invariant, a new binomial coefficient, called the \textit{dot-binomial coefficient} $\binom{n}{k}*{d}$, will be defined. The dot-binomial coefficient $\binom{n}{k}*{d}$ counts the number of $k$-dimensional quadratic subspaces of Euclidean type in $(\mathbb{F}*{q}^{n},x*{1}^{2}+\cdots+x_{n}^{2})$, and behaves like the $q$-binomial coefficient. The similarities and differences between the $q$-binomial coefficient $\binom{n}{k}*{q}$ and the dot-binomial coefficient $\binom{n}{k}*{d}$ will be discussed in this talk. Additionally, I will talk about the relevant combinatorial properties of $\binom{n}{k}_{d}$.

Event contact: hazel dot mcknight at rochester dot edu

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