scholarly journals Oriented Hypergraphs: Introduction and Balance

10.37236/2763 ◽  
2013 ◽  
Vol 20 (3) ◽  
Author(s):  
Lucas J. Rusnak
Keyword(s):  
Incidence Structure ◽  
Complete Classification ◽  
Signed Graph ◽  
Signed Graphs

An oriented hypergraph is an oriented incidence structure that extends the concept of a signed graph. We introduce hypergraphic structures and techniques central to the extension of the circuit classication of signed graphs to oriented hypergraphs. Oriented hypergraphs are further decomposed into three families—balanced, balanceable, and unbalanceable—and we obtain a complete classification of the balanced circuits of oriented hypergraphs.

scholarly journals A Family of Symmetric Graphs with Complete Quotients

10.37236/5701 ◽  
2016 ◽  
Vol 23 (2) ◽  
Author(s):  
Teng Fang ◽  
Xin Gui Fang ◽  
Binzhou Xia ◽  
Sanming Zhou
Keyword(s):  
Complete Graph ◽  
Incidence Structure ◽  
Finite Graph ◽  
Complete Classification ◽  
Complete Graphs ◽  
Quotient Graph ◽  
Point Set ◽  
Natural Incidence ◽  
Ordered Pairs

A finite graph $\Gamma$ is $G$-symmetric if it admits $G$ as a group of automorphisms acting transitively on $V(\Gamma)$ and transitively on the set of ordered pairs of adjacent vertices of $\Gamma$. If $V(\Gamma)$ admits a nontrivial $G$-invariant partition ${\cal B}$ such that for blocks $B, C \in {\cal B}$ adjacent in the quotient graph $\Gamma_{{\cal B}}$ relative to ${\cal B}$, exactly one vertex of $B$ has no neighbour in $C$, then we say that $\Gamma$ is an almost multicover of $\Gamma_{{\cal B}}$. In this case there arises a natural incidence structure ${\cal D}(\Gamma, {\cal B})$ with point set ${\cal B}$. If in addition $\Gamma_{{\cal B}}$ is a complete graph, then ${\cal D}(\Gamma, {\cal B})$ is a $(G, 2)$-point-transitive and $G$-block-transitive $2$-$(|{\cal B}|, m+1, \lambda)$ design for some $m \geq 1$, and moreover either $\lambda=1$ or $\lambda=m+1$. In this paper we classify such graphs in the case when $\lambda = m+1$; this together with earlier classifications when $\lambda = 1$ gives a complete classification of almost multicovers of complete graphs.

scholarly journals Multiplicative automatic sequences

2021 ◽  
Author(s):  
Jakub Konieczny ◽  
Mariusz Lemańczyk ◽  
Clemens Müllner
Keyword(s):  
Complete Classification ◽  
Automatic Sequences ◽  
Complex Valued

AbstractWe obtain a complete classification of complex-valued sequences which are both multiplicative and automatic.

scholarly journals Characteristic cohomology and observables in higher spin gravity

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Alexey Sharapov ◽  
Evgeny Skvortsov
Keyword(s):  
Higher Spin Gravity ◽  
Complete Classification ◽  
Gravity Models ◽  
Simons Theory ◽  
Surface Charges ◽  
Higher Spin ◽  
Dynamical Invariants ◽  
Chern Simons ◽  
Conserved Currents

Abstract We give a complete classification of dynamical invariants in 3d and 4d Higher Spin Gravity models, with some comments on arbitrary d. These include holographic correlation functions, interaction vertices, on-shell actions, conserved currents, surface charges, and some others. Surprisingly, there are a good many conserved p-form currents with various p. The last fact, being in tension with ‘no nontrivial conserved currents in quantum gravity’ and similar statements, gives an indication of hidden integrability of the models. Our results rely on a systematic computation of Hochschild, cyclic, and Chevalley-Eilenberg cohomology for the corresponding higher spin algebras. A new invariant in Chern-Simons theory with the Weyl algebra as gauge algebra is also presented.

scholarly journals Nil-clean quadratic elements

2017 ◽  
Vol 16 (10) ◽  
pp. 1750197 ◽  
Author(s):  
Janez Šter
Keyword(s):  
Complete Classification ◽  
Strong Condition ◽  
Clean Rings

We provide a strong condition holding for nil-clean quadratic elements in any ring. In particular, our result implies that every nil-clean involution in a ring is unipotent. As a consequence, we give a complete classification of weakly nil-clean rings introduced recently in [Breaz, Danchev and Zhou, Rings in which every element is either a sum or a difference of a nilpotent and an idempotent, J. Algebra Appl. 15 (2016) 1650148, doi: 10.1142/S0219498816501486].

Ricci inheritance collineations in Bianchi type II spacetime

2016 ◽  
Vol 31 (17) ◽  
pp. 1650102 ◽  
Author(s):  
Tahir Hussain ◽  
Sumaira Saleem Akhtar ◽  
Ashfaque H. Bokhari ◽  
Suhail Khan
Keyword(s):  
Lie Algebra ◽  
Ricci Tensor ◽  
Bianchi Type ◽  
Complete Classification ◽  
Type Ii

In this paper, we present a complete classification of Bianchi type II spacetime according to Ricci inheritance collineations (RICs). The RICs are classified considering cases when the Ricci tensor is both degenerate as well as non-degenerate. In case of non-degenerate Ricci tensor, it is found that Bianchi type II spacetime admits 4-, 5-, 6- or 7-dimensional Lie algebra of RICs. In the case when the Ricci tensor is degenerate, majority cases give rise to infinitely many RICs, while remaining cases admit finite RICs given by 4, 5 or 6.

scholarly journals Towards a classification of rigid product quotient varieties of Kodaira dimension 0

2021 ◽  
Author(s):  
Ingrid Bauer ◽  
Christian Gleissner
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Structure Theorem ◽  
Complete Classification ◽  
Kodaira Dimension ◽  
The Other ◽  
Diagonal Action ◽  
Quotient Varieties ◽  
A Finite Group

AbstractIn this paper the authors study quotients of the product of elliptic curves by a rigid diagonal action of a finite group G. It is shown that only for $$G = {{\,\mathrm{He}\,}}(3), {\mathbb {Z}}_3^2$$ G = He ( 3 ) , Z 3 2 , and only for dimension $$\ge 4$$ ≥ 4 such an action can be free. A complete classification of the singular quotients in dimension 3 and the smooth quotients in dimension 4 is given. For the other finite groups a strong structure theorem for rigid quotients is proven.

Complete classification of pseudo H-type Lie algebras: I

2017 ◽  
Vol 190 (1) ◽  
pp. 23-51 ◽  
Author(s):  
Kenro Furutani ◽  
Irina Markina
Keyword(s):  
Lie Algebras ◽  
Complete Classification

scholarly journals A Note on the Hierarchy of Quantum Measurement Incompatibilities

Entropy ◽  
2020 ◽  
Vol 22 (2) ◽  
pp. 161
Author(s):  
Bao-Zhi Sun ◽  
Zhi-Xi Wang ◽  
Xianqing Li-Jost ◽  
Shao-Ming Fei
Keyword(s):  
Quantum Mechanics ◽  
Quantum Measurement ◽  
Distinctive Feature ◽  
Complete Classification ◽  
Semidefinite Program

The quantum measurement incompatibility is a distinctive feature of quantum mechanics. We investigate the incompatibility of a set of general measurements and classify the incompatibility by the hierarchy of compatibilities of its subsets. By using the approach of adding noises to measurement operators, we present a complete classification of the incompatibility of a given measurement assemblage with n members. Detailed examples are given for the incompatibility of unbiased qubit measurements based on a semidefinite program.

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