2020/07/07 by Łukaszyk, Szymon
#FOS: Mathematics #General Mathematics (math.GM)
paper · doi:10.48550/arxiv.2007.03782
A short survey on the properties of four graphs constructed in \0, 1\n Boolean space is presented. Flexible activation function of an artificial neuron in a sparse distributed memory model is defined on the basis of the Ugly duckling theorem. Cotan Laplacian on 2-face triangulation of n-cube has degenerate spectrum of eigenvalues corresponding to the Hamming distance distribution of \0, 1\n space. Degenerate spectrum of eigenvalues of the cotan Laplacian defined on the graph comprising 2n 2-face triangulated n-cubes sharing common origin includes all integers from 0 to 3n, without the eigenvalue of 3n-1 (multiplicities of the same eigenvalues form A038717 OEIS sequence), while the multiplicities of the same eigenvalues [-n√(2), n√(2)] of the adjacency matrix of 2n-cube form trinomial triangle. The distance matrix of this graph, providing further OEIS sequences, as well as its relation with Buckminster Fuller vector equilibrium is also discussed.