Related papers: On Finite Racks and Quandles
The structure of groups for which certain sets of commutator subgroups are finite is investigated, with a particular focus on the relationship between these groups and those with finite derived subgroup.
We study generalized regular bent functions using a representation by bent rectangles, that is, special matrices with restrictions on rows and columns. We describe affine transformations of bent rectangles, propose new biaffine and bilinear…
We study rack and quandle coverings from a universal algebraic viewpoint and we show how they can be understood using the notion of strongly abelian congruences. We provide an abstract characterization of several particular types of…
Motivated by the intermediate Lang conjectures on hyperbolicity and rational points, we prove new finiteness results for non-constant morphisms from a fixed variety to a fixed variety defined over a number field by applying Faltings's…
In this note, residual finiteness of quandles is defined and investigated. It is proved that free quandles and knot quandles of tame knots are residually finite and Hopfian. Residual finiteness of quandles arising from residually finite…
We consider a finite universe U (more exactly - a family U of them) and second order quantifiers Q_K, where for each U this means quantifying over a family of n(K)-place relations closed under permuting U. We define some natural orders and…
New identities and congruences involving the ranks and cranks of partitions are proved. The proof depends on a new partial differential equation connecting their generating functions.
We describe a way of representing finite biquandles with n elements as 2n x 2n block matrices. Any finite biquandle defines an invariant of virtual knots through counting homomorphisms. The counting invariants of non-quandle biquandles can…
We prove several new transversality results for formal CR maps between formal real hypersurfaces in complex space. Both cases of finite and infinite type hypersurfaces are tackled in this note.
Permutation rational functions over finite fields have attracted high interest in recent years. However, only a few of them have been exhibited. This article studies a class of permutation rational functions constructed using trace maps on…
We prove that any finitely generated one ended group has linear end depth. Moreover, we give alternative proofs to theorems relating the growth of a finitely generated group to the number of its ends.
In this article, we characterize the (covariant) isotropy groups of free, finitely generated racks and quandles. As a consequence, we show that the usual inner automorphisms of such racks and quandles are precisely those automorphisms that…
We define a class of quandle-like structures called pseudoquandles and analyze some of their algebraic properties.
We give an account on what is known on the subject of permutation matchings, which are bijections of a finite regular semigroup that map each element to one of its inverses. This includes partial solutions to some open questions, including…
The axioms of a quandle imply that the columns of its Cayley table are permutations. This paper studies quandles with exactly one non-trivially permuted column. Their automorphism groups, quandle polynomials, (symmetric) cohomology groups,…
In this paper the notion of Dirac structure in finite dimension is extended to the convenient setting. In particular, we introduce the notion of partial Dirac structure on convenient Lie algebroids and manifolds. We then look for those…
We consider ruled surfaces with finite multiplicity. We study behaviors of the striction curves and the singularities of the ruled surfaces. We also give geometric meanings of invariants related to the ruled surfaces.
New definitions of rack and quandle modules are introduced, and shown to generalise the definitions previously studied by Andruskiewitsch, Etingof and Grana. This new construct is shown to coincide with Beck's general definition of a module…
We define a new algebraic structure called a \emph{pointed rack} and use it to construct ambient isotopy invariants of $ n $-braids. We first introduce an integer-valued invariant of braids using pointed racks. This is then strengthened by…
We establish basic results on subrings of finite commutative rings and closely related rings. Among other applications we calculate the number of maximal subrings of a finite commutative local ring.