Results 11 to 20 of about 44,187 (190)

The Terwilliger algebra of the halved cube

, 2021
Let $D\geq 3$ denote an integer. For any $x\in \mathbb F_2^D$ let $w(x)$ denote the Hamming weight of $x$. Let $X$ denote the subspace of $\mathbb F_2^D$ consisting of all $x\in \mathbb F_2^D$ with even $w(x)$. The $D$-dimensional halved cube $\frac{1}{2}H(D,2)$ is a finite simple connected graph with vertex set $X$ and $x,y\in X$ are adjacent if and ...
Chia-Yi Wen, Hau-Wen Huang
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Quadratic Jordan algebras and cubing operations [PDF]

Transactions of the American Mathematical Society, 1971
In this paper we show how the Jordan structure can be derived from the squaring and cubing operations in a quadratic Jordan algebra, and give an alternate axiomatization of unital quadratic Jordan algebras in terms of operator identities involving only a single variable.
Kevin McCrimmon
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Icosahedral Fibres of the Symmetric Cube and Algebraicity

, 2008
This (second and final) version involves no major changes from the first, but involves a simplification and streamlining of some calculations in Lemma 1.1. To appear in On Certain L-functions Proceedings of a conference in honor of Freydoon Shahidi on his sixtieth birthday Clay Mathematics Proceeedings American Math ...
Dinakar Ramakrishnan
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Modularity of strong normalization and confluence in the algebraic-λ-cube [PDF]

Proceedings Ninth Annual IEEE Symposium on Logic in Computer Science, 2002
Presents the algebraic-/spl lambda/-cube, an extension of Barendregt's (1991) /spl lambda/-cube with first- and higher-order algebraic rewriting. We show that strong normalization is a modular property of all systems in the algebraic-/spl lambda/-cube, provided that the first-order rewrite rules are non-duplicating and the higher-order rules satisfy ...
Franco Barbanera, Maribel Fernández, Herman Geuvers   +2 more
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Poincaré type inequalities on the discrete cube and in the CAR algebra [PDF]

Probability Theory and Related Fields, 2007
We prove Lp Poincare inequalities for functions on the discrete cube and their discrete gradient. We thus recover an exponential inequality and the concentration phenomenon for the uniform probability on the cube first obtained by Bobkov and Gotze. Inequalities involving the discrete gradient and powers of the discrete Laplacian are also considered ...
L. Ben Efraim, F. Lust-Piquard
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The data cube as a typed linear algebra operator [PDF]

Proceedings of The 16th International Symposium on Database Programming Languages, 2017
There is a need for a typed notation for linear algebra applicable to the fields of econometrics and data mining. In this paper we show that such a notation exists and can be useful in formalizing and reasoning about data aggregation operations.One such operation - the construction of a data cube - is shown to be easily expressible as a linear algebra ...
José N. Oliveira, Hugo Daniel Macedo
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ON THE STABLE RANK OF ALGEBRAS OF OPERATOR FIELDS OVER AN $N$-CUBE [PDF]

Bulletin of the London Mathematical Society, 2004
Summary: Let \({\mathcal A}\) be a unital maximal full algebra of operator fields with base space \([0,1]^k\) and fibre algebras \(\{{\mathcal A}_t\}^k_{t\in[0,1]}\). It is shown in this paper that the stable rank of \({\mathcal A}\) is bounded above by the quantity \(\sup_{t\in[0,1]^k}\text{sr}(C([0,1]^k)\otimes{\mathcal A}_t)\), where `sr' means ...
Ping Wong Ng, Takahiro Sudo
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Algebraic cycles and EPW cubes [PDF]

Mathematische Nachrichten, 2018
AbstractLet X be a hyperkähler variety with an anti‐symplectic involution ι. According to Beauville's conjectural “splitting property”, the Chow groups of X should split in a finite number of pieces such that the Chow ring has a bigrading. The Bloch–Beilinson conjectures predict how ι should act on certain of these pieces of the Chow groups.
Robert Laterveer
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Ternary Associativity and Ternary Lie Algebra at Cube Root of Unity [PDF]

Axioms
We propose a new approach to extending the notion of commutator and Lie algebra to algebras with ternary multiplication laws. Our approach is based on ternary associativity of the first and second kind. We propose a ternary commutator, which is a linear combination of six (all permutations of three elements) triple products.
Viktor Abramov
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Existence of cube terms in finite algebras [PDF]

Algebra universalis, 2019
We study the problem of whether a given finite algebra with finitely many basic operations contains a cube term; we give both structural and algorithmic results. We show that if such an algebra has a cube term then it has a cube term of dimension at most $N$, where the number $N$ depends on the arities of basic operations of the algebra and the size of
Alexandr Kazda, Dmitriy Zhuk
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