Jan Florek

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20182025

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3 papers · 1 filter

math.CO2025

Kempe equivalence of 4-colourings of some plane triangulations

Jan Florek

Let $G_{n}$ , where $n ⩾ 5$ , be a simple plane triangulation which has $2$ non-adjacent vertices of degree $n$ (called \textit{poles} of $G_{n}$ ) and $2 n$ vertices of degree~$…

math.RT2025

Relative Serre duality for Hecke categories

Quoc P. Ho, Penghui Li

We prove a conjecture of Gorsky, Hogancamp, Mellit, and Nakagane in the Weyl group case. Namely, we show that the left and right adjoints of the parabolic induction functor between…

math.CO2025

On Dirac and Motzkin problem in discrete geometry

Jan Florek

Dirac and Motzkin conjectured that any set X of $n$ non-collinear points in the plane has an element incident with at least $⌈ \frac{n}{2} ⌉$ lines spanned by X. In this…