7 papers
Complexity of Low-Degree Skew Polynomial Multiplication over Finite Fields
Ke Ye, Yichuan Cao, Ruichen Qiu
In this note, we study the complexity of multiplication in skew polynomial rings over finite fields. We prove that the product of two elements in of degree…
Geometry of multilinear varieties over infinite fields and its applications
Qiyuan Chen, Ke Ye
Multilinear varieties, defined as the sets of rational points of varieties cut out by multilinear functions, were first introduced and studied by Gowers and Milićević[Proc. Edinb.…
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…
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.…
A quasi-optimal lower bound for skew polynomial multiplication
Qiyuan Chen, Ke Ye
We establish a lower bound for the complexity of multiplying two skew polynomials. The lower bound coincides with the upper bound conjectured by Caruso and Borgne in 2017, up to a…