Zobrazeno 1 - 10
of 405
pro vyhledávání: '"15A75"'
Autor:
Traves, Will
A solution is provided to the Bruxelles Problem, a geometric decision problem originally posed in 1825, that asks for a synthetic construction to determine when ten points in 3-space lie on a quadric surface, a surface given by the vanishing of a deg
Externí odkaz:
http://arxiv.org/abs/2412.05678
Publikováno v:
Linear and Multilinear Algebra vol 67, issue 5 (2019), pages 939-952
Let $\mathbb{F}$ be a field of characteristic $\neq 2$ and $3$, let $V$ be a $\mathbb{F}$-vector space of dimension $6$, and let $\Omega \in \wedge ^2V^\ast $ be a non-degenerate form. A system of generators for polynomial invariant functions under t
Externí odkaz:
http://arxiv.org/abs/2412.03135
Autor:
Canepa, Giovanni
We consider injectivity and surjectivity of some maps on the exterior algebra of isomorphic finite-dimensional vector spaces. We prove the properties of the maps in full generality, for any dimension of the vector space and any subspace. We also draw
Externí odkaz:
http://arxiv.org/abs/2410.17682
Autor:
Gatto, Letterio, Yousofzadeh, Malihe
The Clifford algebra of the endomorphisms of the exterior algebra of a countably dimensional vector space induces natural bosonic shadows, i.e. families of linear maps between the cohomologies of complex grassmannians. The main result of this paper i
Externí odkaz:
http://arxiv.org/abs/2410.15152
Autor:
Vannieuwenhoven, Nick
A numerical algorithm to decompose a low-rank skew-symmetric tensor into a sum of elementary (rank-$1$) skew-symmetric tensors is introduced. The algorithm uncovers this Grassmann decomposition based on linear relations that are encoded by the kernel
Externí odkaz:
http://arxiv.org/abs/2410.14486
Recent work of Scott and Wilmer and of Woodroofe extends the Erd\H{o}s-Ko-Rado theorem from set systems to subspaces of k-forms in an exterior algebra. We prove an extension of the Hilton-Milner theorem to the exterior algebra setting, answering in a
Externí odkaz:
http://arxiv.org/abs/2406.17857
We show that modeling a Grassmannian as symmetric orthogonal matrices $\operatorname{Gr}(k,\mathbb{R}^n) \cong\{Q \in \mathbb{R}^{n \times n} : Q^{\scriptscriptstyle\mathsf{T}} Q = I, \; Q^{\scriptscriptstyle\mathsf{T}} = Q,\; \operatorname{tr}(Q)=2k
Externí odkaz:
http://arxiv.org/abs/2406.11821
Autor:
Hegedüs, Gábor
Let $t$ be a non-negative integer and $\mbox{$\cal P$}=\{(A_i,B_i)\}_{1\leq i\leq m}$ be a set-pair family satisfying $|A_i \cap B_i|\leq t$ for $1\leq i \leq m$. $\mbox{$\cal P$}$ is called strong Bollob\'as $t$-system, if $|A_i\cap B_j|>t$ for all
Externí odkaz:
http://arxiv.org/abs/2406.05841
Autor:
Lee, Soo Teck, Zhang, Ruibin
We develop an algebraic approach to the branching of representations of the general linear Lie superalgebra $\mathfrak{gl}_{p|q}({\mathbb C})$, by constructing certain super commutative algebras whose structure encodes the branching rules. Using this
Externí odkaz:
http://arxiv.org/abs/2403.11393
Autor:
Mandolesi, André L. G.
Complex determinants, Gramians and blades (simple or decomposable multivectors) are related to volumes, but not in the same way as real ones. We present their complete geometric interpretations, including complex orientations. We also link real and c
Externí odkaz:
http://arxiv.org/abs/2403.17022