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of 38
pro vyhledávání: '"Conner, Austin"'
In this paper, we settle a conjecture due to Sturmfels and Uhler concerning generation of the prime ideal of the variety associated to the Gaussian graphical model of any cycle graph. Our methods are general and applicable to a large class of ideals
Externí odkaz:
http://arxiv.org/abs/2308.05561
We provide a complete description of the ideal that serves as the resultant ideal for n univariate polynomials of degree d. We in particular describe a set of generators of this resultant ideal arising as maximal minors of a set of cascading matrices
Externí odkaz:
http://arxiv.org/abs/2306.02085
Autor:
Conner, Austin, Michałek, Mateusz
We introduce the characteristic numbers and the chromatic polynomial of a tensor. Our approach generalizes and unifies the chromatic polynomial of a graph and of a matroid, characteristic numbers of quadrics in Schubert calculus, Betti numbers of com
Externí odkaz:
http://arxiv.org/abs/2111.00809
We determine the border ranks of tensors that could potentially advance the known upper bound for the exponent $\omega$ of matrix multiplication. The Kronecker square of the small $q=2$ Coppersmith-Winograd tensor equals the $3\times 3$ permanent, an
Externí odkaz:
http://arxiv.org/abs/2009.11391
Let $M_{\langle u,v,w\rangle}\in C^{uv}\otimes C^{vw}\otimes C^{wu}$ denote the matrix multiplication tensor (and write $M_n=M_{\langle n,n,n\rangle}$) and let $det_3\in ( C^9)^{\otimes 3}$ denote the determinant polynomial considered as a tensor. Fo
Externí odkaz:
http://arxiv.org/abs/1911.07981
We classify tensors with maximal and next to maximal dimensional symmetry groups under a natural genericity assumption (1-genericity), in dimensions greater than 7. In other words, we classify minimal dimensional orbits in the space of (m,m,m) tensor
Externí odkaz:
http://arxiv.org/abs/1909.09518
Publikováno v:
computational complexity, 31 (1), 2022
We prove that the border rank of the Kronecker square of the little Coppersmith-Winograd tensor $T_{cw,q}$ is the square of its border rank for $q > 2$ and that the border rank of its Kronecker cube is the cube of its border rank for $q > 4$. This an
Externí odkaz:
http://arxiv.org/abs/1909.04785
Autor:
Conner, Austin1 (AUTHOR), Huang, Hang2 (AUTHOR), Landsberg, J. M.3 (AUTHOR) jml@math.tamu.edu
Publikováno v:
Foundations of Computational Mathematics. Dec2023, Vol. 23 Issue 6, p2049-2087. 39p.
Publikováno v:
Collectanea Mathematica, 2020
We make a first geometric study of three varieties in $\mathbb{C}^m \otimes \mathbb{C}^m \otimes \mathbb{C}^m$ (for each $m$), including the Zariski closure of the set of tight tensors, the tensors with continuous regular symmetry. Our motivation is
Externí odkaz:
http://arxiv.org/abs/1811.05511
Autor:
Conner, Austin
The recent discovery that the exponent of matrix multiplication is determined by the rank of the symmetrized matrix multiplication tensor has invigorated interest in better understanding symmetrized matrix multiplication. I present an explicit rank 1
Externí odkaz:
http://arxiv.org/abs/1711.05796