Related papers: A conjecture on superconnected quandles

A typical concept in quantum state analysis is based on the idea that states in the vicinity of some pure entangled state share the same properties; implying that states with a high fidelity must be entangled. States whose entanglement can…

Characteristic properties of corings with a grouplike element are analysed. Associated differential graded rings are studied. A correspondence between categories of comodules and flat connections is established. A generalisation of the…

We prove that a countable simple unidimensional theory that eliminates hyperimaginaries is supersimple. This solves a problem of Shelah in the more general context of simple theories under weak assumptions.

In this paper, we achieve some interesting results in the way to make sense how superparticles interact together and to ordinary particles by means of putting aside the dimensional constraints. This is the first step in the process of…

Let G be a semisimple complex algebraic group, and H a wonderful subgroup of G. We prove several results relating the subgroup H to the properties of a combinatorial invariant S of G/H, called its spherical system. It is also possible to…

The undirected technique for evaluating belief networks [Jensen, et.al., 1990, Lauritzen and Spiegelhalter, 1988] requires clustering the nodes in the network into a junction tree. In the traditional view, the junction tree is constructed…

In the present paper, we introduce the new construction of quandles. For a group $G$ and its subset $A$ we construct a quandle $Q(G,A)$ which is called the $(G,A)$-quandle and study properties of this quandle. In particular, we prove that…

In this paper, we investigate the residual finiteness and subquandle separability of quandles, properties that respectively imply the solvability of the word problem and the generalized word problem for quandles. From Winker's work, we know…

Couplings between a closed string RR field and open strings are calculated in a system of coincident branes and antibranes of type II theory. The result can be written cleanly using the curvature of the superconnection.

The Mordell-Lang conjecture describes the intersection of a finitely generated subgroup with a closed subvariety of a semiabelian variety. Equivalently, this conjecture describes the intersection of closed subvarieties with the set of…

We restructure and advance the classification theory of finite racks and quandles by employing powerful methods from transformation groups and representation theory, especially Burnside rings. These rings serve as universal receptacles for…

In the framework of algebraic supergeometry, we give a construction of the scheme-theoretic supergeometric analogue of Chevalley groups, namely affine algebraic supergroups associated to simple Lie superalgebras of classical type. In…

In this paper we propose a conjecture concerning partial sums of an arbitrary finite subset of an abelian group, that naturally arises investigating simple Heffter systems. Then, we show its connection with related open problems and we…

We prove a few simple cases of a random graph statement that would imply the "second" Kahn--Kalai Conjecture. Even these cases turn out to be reasonably challenging, and it is hoped that the ideas introduced here may lead to further…

The paper contains a general construction which produces new examples of non simply-connected smooth projective surfaces. We analyze the resulting surfaces and their fundamental groups. Many of these fundamental groups are expected to be…

We discuss a construction that gives counterexamples to various questions of unique determination of convex bodies.

It is the purpose of this note to classify connected quandles up to order 14, and in particular to show that there is no connected quandle of order 14.

We classify simple finite Jordan conformal superalgebras and establish preliminary results for the classification of simple finite Jordan pseudoalgebras.

We present an overview of some older papers on involutory quandles, mostly from the times before the term "quandle" was born. It is meant as a reference guide, not (yet) as an expository article explaining what the involutory quandles are…

In 2016, Leclerc constructed conjectural cluster structures on open Richardson varieties using representations of preprojective algebras. A variant with more explicit seeds was obtained by M\'enard in his thesis. We show that M\'enard's…