A Hadamard matrix is balanced splittable if some subset of its rows has the property that dot product every two distinct columns takes at most values. This definition was introduced by Kharaghani and Suda in 2019, although equivalent formulations have been previously studied using different terminology. We collate previous results phrased terms matrices, real flat equiangular tight frames, sphe...

Let $n$ be the order of a quaternary Hadamard matrix. It is shown that existence projective plane equivalent to balancedly multi-splittable matrix $n^2$.

In single chip multiprocessors (CMP) with grid topologies, a significant part of power consump-tion is attributed to communications between the cores of the grid. We investigate the problem ofrouting communications between CMP cores using shortest paths, in a model in which the powercost associated with activating a communication link at a transmission speed of f bytes/second is...

We describe the modules Dλ↓Σn−1 and D λ↑n+1 for certain simple KΣn-modules (completely splittable and some close to) D, where K is a field of characteristic p > 0 and Σn is the symmetric group of degree n. This result is based on an upper bound of the dimensions of the Ext-spaces between some simple modules.