We prove that the propositional translations of the KneserLovász theorem have polynomial size extended Frege proofs and quasipolynomial size Frege proofs. We present a new counting-based combinatorial proof of the Kneser-Lovász theorem that avoids the topological arguments of prior proofs. We introduce a miniaturization of the octahedral Tucker lemma, called the truncated Tucker lemma. The prop...

For the approximation of time-dependent data tensors and of solutions to tensor differential equations by tensors of low Tucker rank, we study a computational approach that can be viewed as a continuous-time updating procedure. This approach works with the increments rather than the full tensor and avoids the computation of decompositions of large matrices. In this method, the derivative is pro...

The Octahedral Tucker problem considers an n-dimensional hypergrid of side length two, centered at the origin, triangulated by connecting the origin to all outside vertices (applied recursively on each of the lower dimensional hypergrids passing through their origins at the corresponding reduced dimensions). Each vertex is assigned a color in ±i : i = 1, 2, ..., n computed using a polynomial si...