David Tom Foss

Three Disjoint Boolean Balls for Every Tripartition Tensor: Explicit Rank Decompositions, the Exact Rank of T(1,1,c), Depth-One Decompositions and Barriers at Rate 8

We give an explicit rank decomposition of every tripartition tensor. For a, b, c ≥ 1 and N = a + b + c, the tensor T_{a,b,c} of ordered partitions of an N-set into an a-, a b- and a c-set satisfies, over every field of characteristic ≠ 2, R(T_{a,b,c}) ≤ 2^(N−1) − Σ_{r ∈ {a,b,c}}...