Related papers: Orbits and self-twuality in set systems and delta-…
A Delta-groupoid is an algebraic structure which axiomitizes the combinatorics of a truncated tetrahedron. It is shown that there are relations of Delta-groupoids to rings, group pairs, and (ideal) triangulations of three-manifolds. In…
We establish a connection between the algebraic geometry of the type B permutohedral toric variety and the combinatorics of delta-matroids. Using this connection, we compute the volume and lattice point counts of type B generalized…
We present a new case of duality between integrable many-body systems, where two systems live on the action-angle phase spaces of each other in such a way that the action variables of each system serve as the particle positions of the other…
We initiate the axiomatic study of affine oriented matroids (AOMs) on arbitrary ground sets, obtaining fundamental notions such as minors, reorientations and a natural embedding into the frame work of Complexes of Oriented Matroids. The…
In the paper "Aquino, C., Jim\'enez, R., Mijangos, M., Morales Mel\'endez, Q.: On Invariant (co)homology of a group, preprint" are introduced two groups generated by the orbits of an action of a group on another group by automorphisms. One…
We investigate the structure and properties of symmetric ideals generated by general forms in the polynomial ring under the natural action of the symmetric group. This work significantly broadens the framework established in our earlier…
This article initiates a geometric study of the automorphism groups of general graph products of groups, and investigates the algebraic and geometric structure of automorphism groups of cyclic product of groups. For a cyclic product of at…
Taking into account the recent developments associated with duality in physics, this article is focused on investigating the properties of a tensor generalization of the electrodynamics dual to the standard vector model even considering the…
In this note we extend the concept of topological stability from homeomorphisms to group actions on compact metric spaces, and prove that if an action of a finitely generated group is expansive and has the pseudo-orbit tracing property then…
This is a survey of recent progress in several areas of combinatorial algebra. We consider combinatorial problems about free groups, polynomial algebras, free associative and Lie algebras. Our main idea is to study automorphisms and, more…
We introduce the {\it Ellis semigroup} of a nonautonomous discrete dynamical system $(X,f_{1,\infty})$ when $X$ is a metric compact space. The underlying set of this semigroup is the pointwise closure of $\{f\sp{n}_1 \, |\, n\in…
Computational problems concerning the orbit of a point under the action of a matrix group occur throughout computer science, including in program analysis, complexity theory, quantum computation, and automata theory. In many cases the focus…
The wreath product of two permutation groups G < Sym(Gamma) and H < Sym(Delta) can be considered as a permutation group acting on the set Pi of functions from Delta to Gamma. This action, usually called the product action, of a wreath…
The space of smooth sections of a symplectic fiber bundle carries a natural symplectic structure. We provide a general framework to determine the momentum map for the action of the group of bundle automorphism on this space. Since, in…
We primarily investigate the properties of characteristic polynomials of semimatroids. In particular, we provide a combinatorial interpretation of their coefficients, generalizing the Whitney's Broken Circuit Theorem. We also prove that the…
In the paper the foundation of the $k$-orbit theory is developed. The theory opens a new simple way to the investigation of groups and multidimensional symmetries. The relations between combinatorial symmetry properties of a $k$-orbit and…
Takahasi's theorem on chains of subgroups of bounded rank in a free group is generalized to several classes of semigroups. As an application, it is proved that the subsemigroups of periodic points are finitely generated and periodic orbits…
We consider a version of the notion of F-inverse semigroup (studied in the algebraic theory of inverse semigroups). We point out that an action of such an inverse semigroup on a locally compact space has associated a natural groupoid…
In 2024, Ceballos and Chenevi{\`e}re introduced alt $\nu$-Tamari lattices, parameterized by a lattice path $\nu$ and an increment vector $\delta$, as a common generalization of $\nu$-Tamari and $\nu$-Dyck lattices. We study rowmotion on two…
Binary delta-matroids are closed under vertex flips, which consist of the natural operations of twist and loop complementation. In this note we provide an extension of this result from GF(2) to GF(4). As a consequence, quaternary matroids…