5 papers · 1 filter
Turán problems for multilinear maps
Qiyuan Chen, Zixiang Xu, Ke Ye
We study Turán-type extremal problems for alternating and unrestricted multilinear maps. For alternating order- multilinear maps , we determi…
Isotropy and completeness indices of multilinear maps
Qiyuan Chen, Ke Ye
Structures of multilinear maps are characterized by invariants. In this paper we introduce two invariants, named the isotropy index and the completeness index. These invariants cap…
Extremal constructions for apex partite hypergraphs
Qiyuan Chen, Hong Liu, Ke Ye
We establish new lower bounds for the Turán and Zarankiewicz numbers of certain apex partite hypergraphs. Given a -partite -uniform hypergraph , let $\ma…
Bounds for Geometric rank in Terms of Subrank
Qiyuan Chen, Ke Ye
For tensors of fixed order, we establish three types of upper bounds for the geometric rank in terms of the subrank. Firstly, we prove that, under a mild condition on the character…
Stability of ranks under field extensions
Qiyuan Chen, Ke Ye
This paper studies the stability of tensor ranks under field extensions. Our main contributions are fourfold: (1) We prove that the analytic rank is stable under field extensions.…