2 papers
math.CO2021
Tensor slice rank and Cayley's first hyperdeterminant
Alimzhan Amanov, Damir Yeliussizov
Cayley's first hyperdeterminant is a straightforward generalization of determinants for tensors. We prove that nonzero hyperdeterminants imply lower bounds on some types of tensor…
math.CO2020
MacMahon's statistics on higher-dimensional partitions
Alimzhan Amanov, Damir Yeliussizov
We study some combinatorial properties of higher-dimensional partitions which generalize plane partitions. We present a natural bijection between -dimensional partitions and …