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math.CO2023
Quantitative Transversal Theorems in the Plane
Ilani Axelrod-Freed, João Pedro Carvalho, Yuki Takahashi
Hadwiger's theorem is a Helly-type theorem involving common transversals to families of convex sets instead of common intersections. Subsequently, Pollack and Wenger identified a n…
math.CO2021
Enumerating -Naples Parking Functions Through Catalan Objects
João Pedro Carvalho, Pamela E. Harris, Gordon Rojas Kirby +2
This paper studies a generalization of parking functions named -Naples parking functions, where backward movement is allowed. One consequence of backward movement is that the nu…
math.CO2021
Counterexamples to the Colorful Tverberg Conjecture for Hyperplanes
João Pedro Carvalho, Pablo Soberón
In 2008 Karasev conjectured that for every set of blue lines, green lines, and red lines in the plane, there exists a partition of them into colorful triples whose…