A. Schilling

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math.CO2026

Dimension of splines on graphs in the case of degree two and smoothness one in two variables

Shaheen Nazir, Anne Schilling, Julianna Tymoczko

Continuous spline functions are defined as piecewise polynomials on the faces of a polyhedral complex that agree on the intersections of two faces. Splines are used in approximatio…

math.CO2024

The immersion poset on partitions

Lisa Johnston, David Kenepp, Evuilynn Nguyen +4

We introduce the immersion poset $(P (n), ⩽_{I})$ on partitions, defined by $I^» ⩽_{I} I^¼$ if and only if $s_{I^} ¼ (x_{1}, \dots, x_{N}) - s_{I^} » (x_{1}, \dots, x_{N})$ is mo…