text: 152,129,1282592569243971584,1192152664412475393,Fulvio Gesmundo,"A lot of examples of strict subadditivity of tensor border rank under direct sum! Check out our new paper with M. Christandl, M. Michałek and J. Zuiddam (@jzuiddam): ""Border rank non-additivity for higher order tensors"" <LINK> In 1981, Schönhage provided examples of strict subadditivity of border rank under direct sum for tensors of order three. His example was a stepping stone to all subsequent progress on upper bounds on the matrix multiplication exponent until today. We provide examples of strict subadditivity for higher order tensors with connections to tensor network geometry and the complexity theory of generalizations of the matrix multiplication tensor.",https://arxiv.org/abs/2007.05458,"Whereas matrix rank is additive under direct sum, in 1981 Sch\""onhage showed that one of its generalizations to the tensor setting, tensor border rank, can be strictly subadditive for tensors of order three. Whether border rank is additive for higher order tensors has remained open. In this work, we settle this problem by providing analogs of Sch\""onhage's construction for tensors of order four and higher. Sch\""onhage's work was motivated by the study of the computational complexity of matrix multiplication; we discuss implications of our results for the asymptotic rank of higher order generalizations of the matrix multiplication tensor. ",Border rank non-additivity for higher order tensors,3,"['A lot of examples of strict subadditivity of tensor border rank under direct sum! Check out our new paper with M. Christandl, M. Michałek and J. Zuiddam (@jzuiddam):\n\n""Border rank non-additivity for higher order tensors""\n\n<LINK>', 'In 1981, Schönhage provided examples of strict subadditivity of border rank under direct sum for tensors of order three. His example was a stepping stone to all subsequent progress on upper bounds on the matrix multiplication exponent until today.', 'We provide examples of strict subadditivity for higher order tensors with connections to tensor network geometry and the complexity theory of generalizations of the matrix multiplication tensor.']",20,07,669