相关论文: Triple symbols in arithmetic

Three-way dissimilarities are a generalization of (two-way) dissimilarities which can be used to indicate the lack of homogeneity or resemblance between any three objects. Such maps have applications in cluster analysis, and have been used…

We describe the symbolic calculus of operators on the unit sphere in the complex n-space $\mathbb C^n$ defined by the Berezin quantization. In particular, we derive a explicit formula for the composition of Berezin symbol and with that a…

In a recent article (arXiv:1507.03499) (joint with Alon Regev) we studied sums of squares of characters Chi(L,M) of the Symmetric Group over shapes L that are two-rowed, and shapes L that are hook shapes, and M is an arbitrary shape that…

In this paper we state and prove the analogous of the principal ideal theorem of algebraic number theory for the case of 3-manifolds from the point of view of arithmetic topology.

The paper presents a systematic construction of primitive Pythagorean triples. The order of enumeration on the set of primitive Pythagorean triples is defined. The order is based on the representation of a primitive Pythagorean triple by…

Our constructions provide a systematic way to study cohomology tri-dendriform algebra via classical cohomology, simplifying computations and enabling the use of established techniques.

We compute the integral cohomology rings of a family of 3-groups. As a corollary, we exhibit, for each n greater than or equal to 5, a pair of groups of order 3^n whose integral cohomology rings are isomorphic.

We describe a construction that takes as input a graph and a basis for its first homology, and returns a triangulation of a 3-dimensional homology sphere. This makes precise an idea of M. Gromov and A. Nabutovski. The immediate application,…

The graphs with permutation-representation number (\textit{prn}) at most two are known. While a characterization for the class of graphs with the \textit{prn} at most three is an open problem, we summarize the graphs of this class that are…

Alternating sign triangles were introduced by Carroll and Speyer in relation to cube recurrence, by analogy to alternating sign matrices for octahedron recurrence. Permutation triangles are the alternating sign triangles whose entries are…

We examine what integers are representable as sums of three cubes. We also provide formulas for the number of representations of $x^3+y^3+z^3=n$ under the condition $x+y+z=t$. Also we show how the problem of three cubes is related to…

The Hermitian decomposition of a linear operator is generalized to the case of two or more operations. An additive expansion of the product of three octonions into three parts is constructed, wherein each part either preserve or change the…

We study homology and cohomology of triassociative algebras with non-trivial coefficients.

For a triple $(G,A,\kappa)$ (where $G$ is a group, $A$ is a $G$-module and $\kappa:G^3\to A$ is a 3-cocycle) and a $G$-module $B$ we introduce a new cohomology theory $_2H^n(G,A,\kappa;B)$ which we call the secondary cohomology. We give a…

We introduce the Habiro ring of a number field $\mathbb{K}$ and modules over it graded by $K_3(\mathbb{K})$. Elements of these modules are collections of power series at each complex root of unity that arithmetically glue with each other…

We establish the formula for multiplication by the class of a special Schubert variety in the integral cohomology ring of the flag manifold. This formula also describes the multiplication of a Schubert polynomial by either an elementary…

In this paper, we consider a 3-Lie algebra with a derivation (called a 3-LieDer pair). We define cohomology for a 3-LieDer pair with coefficients in a representation. We use this cohomology to study deformations and abelian extensions of…

A permutation graph is a graph that can be derived from a permutation, where the vertices correspond to letters of the permutation, and the edges represent inversions. We provide a construction to show that there are infinitely many…

Periodic tangles are 1-dimensional submanifolds in the 3-space with translational symmetry. In this paper, we define the linking numbers for singly, doubly, and triply periodic tangles using appropriate motifs and show that they are…

We define a triangle design as a partition of the set of lines of a projective space into triangles, where a triangle consists of three pairwise intersecting lines with no common point. A triangle design is balanced if all points are…