Simulating Asymptotic Orders of the Number of Graphical Partitions and Graphical Degree Sequences
Kai Wang, Troy Purvis · 2018
We design randomized algorithms to simulate the currently unknown asymptotic orders of the number of graphical degree sequences of given length and the number of graphical partitions of a given even integer. Computational simulations are conducted and the obtained simulation data are analyzed using the method of nonlinear least squares to derive conjectures about the asymptotic orders of the two considered combinatorial functions. These conjectures can be used to estimate the values of these functions when inputs are large and can compare against future rigorous asymptotic analysis of these functions.