For any simplicial complex, the sum of the k largest upper-Laplacian eigenvalues is at most the sum of the (r+1)k largest r-degrees of (r-1)-faces, with applications to graphs and partite complexes.
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Sums of Laplacian eigenvalues and sums of degrees
For any simplicial complex, the sum of the k largest upper-Laplacian eigenvalues is at most the sum of the (r+1)k largest r-degrees of (r-1)-faces, with applications to graphs and partite complexes.