Related papers: Decomposition Complexes
We consider path ideals associated to special classes of posets such as tree posets and cycles. We express their property of being sequentially Cohen-Macaulay in terms of the underlying poset. Moreover, monomial ideals, which arise from the…
From a group action on a space, define a variant of the configuration space by insisting that no two points inhabit the same orbit. When the action is almost free, this "orbit configuration space" is the complement of an arrangement of…
An order-theoretic generalization of Seymour relations describing the connection between the set-theoretic blocker, deletion, and contraction maps on clutters, is presented.
We look at generalized complex structures from the point of view of Poisson and Dirac geometry and we remark that the puzzling equations underlying the notion of generalized complex structure have miraculously simple meaning when passing to…
In this paper we show that the set of closure relations on a finite poset P forms a supersolvable lattice, as suggested by Rota. Furthermore this lattice is dually isomorphic to the lattice of closed sets in a convex geometry (in the sense…
We study classes of objects whose combinatorics are closely related to those of posets. The framework of operads and operad algebras allows us to make this relationship precise and provides tools for a deeper understanding of their…
We introduce several new constructions of finite posets with the number of linear extensions given by generalized continued fractions. We apply our results to the problem of the minimum number of elements needed for a poset with a given…
We propose a simple approach to formal deformations of associative algebras. It exploits the machinery of multiplicative coresolutions of an associative algebra A in the category of A-bimodules. Specifically, we show that certain…
In this paper, we study the posets of classes of subgroups of finite group having same set of orders of elements. We show that this poset is a chain only in the case of p-groups and moreover, we characterize all finite groups for which this…
A set of general physical principles is proposed as the structural basis for the theory of complex systems. First the concept of harmony is analyzed and its different aspects are uncovered. Then the concept of reflection is defined and…
In this paper we outline the application of decomposition to condensation defects and their fusion rules. Briefly, a condensation defect is obtained by gauging a higher-form symmetry along a submanifold, and so there is a natural interplay…
The group invariance of entanglement is obtained within a very general and simple setup of the latter, given by a recently introduced considerably extended concept of tensor products. This general approach to entanglement - unlike the usual…
We introduce decomposition algebras as a natural generalization of axial algebras, Majorana algebras and the Griess algebra. They remedy three limitations of axial algebras: (1) They separate fusion laws from specific values in a field,…
In this paper we present the novel qualities of entanglement of formation for general (so also infinite dimensional) quantum systems. A major benefit of our presentation is a rigorous description of entanglement of formation. In particular,…
An expository summary of properties of the poset of Dyck paths ordered by inclusion.
The kinematical part of general theory of deformational structures on smooth manifolds is developed. We introduce general concept of d-objects deformation, then within the set of all such deformations we develop some special algebra and…
A combinatorial study of multiple $q$-integrals is developed. This includes a $q$-volume of a convex polytope, which depends upon the order of $q$-integration. A multiple $q$-integral over an order polytope of a poset is interpreted as a…
Motivated by the idea of using simple macroscopic examples to illustrate the physics of complex systems, we modify a historic experimental setup in which interacting floating magnets spontaneously self-assemble into ordered clusters. By…
The interleaving distance, although originally developed for persistent homology, has been generalized to measure the distance between functors modeled on many posets or even small categories. Existing theories require that such a poset…
We present a new fragment of axiomatic set theory for pure sets and for the iteration of power sets within given transitive sets. It turns out that this formal system admits an interesting hierarchy of models with true membership relation…