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math.CO2020
Sequence Positivity Through Numeric Analytic Continuation: Uniqueness of the Canham Model for Biomembranes
Stephen Melczer, Marc Mezzarobba
We prove solution uniqueness for the genus one Canham variational problem arising in the shape prediction of biomembranes. The proof builds on a result of Yu and Chen that reduces…
math.CO2020
Asymptotic bounds on graphical partitions and partition comparability
Stephen Melczer, Marcus Michelen, Somabha Mukherjee
An integer partition is called graphical if it is the degree sequence of a simple graph. We prove that the probability that a uniformly chosen partition of size is graphical de…