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math.HO2024
Colorful Rings of Partition
Oliver Knill
We visualize the identity p(n) = sum s(k) p(n-k)/n for the integer partition function p(n) involving the divisor function s, add comments on the history of visualizations of number…
math.CO2024
Gauss-Bonnet for Form Curvatures
Oliver Knill
We look at curvatures that are supported on k-dimensional parts of a simplicial complex G. These curvature all satisfy the Gauss-Bonnet theorem, provided that the k-dimensional sim…
math.CO2024
Fusion inequality for quadratic cohomology
Oliver Knill
Classical simplicial cohomology on a simplicial complex G deals with functions on simplices x in G. Quadratic cohomology deals with functions on pairs of simplices (x,y) in G x G t…