Related papers: Interval decomposition lattices are balanced
We are interested in the problem of translating between two representations of closure systems, namely implicational bases and meet-irreducible elements. Albeit its importance, the problem is open. Motivated by this problem, we introduce…
We consider overdetermined systems of difference equations for a single function $u$ which are consistent, and propose a general framework for their analysis. The integrability of such systems is defined as the existence of higher order…
We study arrangements of intervals in $\mathbb{R}^2$ for which many pairs form trapezoids. We show that any set of intervals forming many trapezoids must have underlying algebraic structure, which we characterise. This leads to some…
Let $A$ be a, not necessarily closed, linear relation in a Hilbert space $\sH$ with a multivalued part $\mul A$. An operator $B$ in $\sH$ with $\ran B\perp\mul A^{**}$ is said to be an operator part of $A$ when $A=B \hplus (\{0\}\times \mul…
Each family $\mathcal{M}$ of means has a natural, partial order (point-wise order), that is $M \le N$ iff $M(x) \le N(x)$ for all admissible $x$. In this setting we can introduce the notion of interval-type set (a subset $\mathcal{I}…
This paper studies the differential lattice, defined to be a lattice $L$ equipped with a map $d:L\to L$ that satisfies a lattice analog of the Leibniz rule for a derivation. Isomorphic differential lattices are studied and classifications…
Every lattice is isomorphic to a lattice whose elements are sets of sets, and whose operations are intersection and an operation extending the union of two sets of sets A and B by the set of all sets in which the intersection of an element…
A mixed lattice vector space is a partially ordered vector space with two partial orderings and certain lattice-type properties. In this paper we first give some fundamental results in mixed lattice groups, and then we investigate the…
A residuated lattice is defined to be integrally closed if it satisfies the equations x\x = e and x/x = e. Every integral, cancellative, or divisible residuated lattice is integrally closed, and, conversely, every bounded integrally closed…
We propose a classification of group properties according to whether they can be deduced from the assumption that a group's subgroup lattice contains an interval isomorphic to some lattice. We are able to classify a few group properties as…
The decomposition into interaction subspaces is an important result for graphical models and plays a central role for results on the linearized marginal problem; similarly the Chaos decomposition plays an important role in statistical…
Interval graphs and interval orders are deeply linked. In fact, edges of an interval graphs represent the incomparability relation of an interval order, and in general, of different interval orders. The question about the conditions under…
Intertwiners between \ade lattice models are presented and the general theory developed. The intertwiners are discussed at three levels: at the level of the adjacency matrices, at the level of the cell calculus intertwining the face…
The paper proposes a general notion of interaction between attributes, which can be applied to many fields in decision making and data analysis. It generalizes the notion of interaction defined for criteria modelled by capacities, by…
In this paper we completely characterize lattice ideals that are complete intersections or equivalently complete intersections finitely generated semigroups of $\bz^n\oplus T$ with no invertible elements, where $T$ is a finite abelian…
In this paper, we have established boundaries of cardinal numbers of nonempty sets in finite non-$T_1$ topological spaces using interval analysis. For a finite set with known cardinality, we give interval estimations based on the closure…
Dualization of a monotone Boolean function on a finite lattice can be represented by transforming the set of its minimal 1 to the set of its maximal 0 values. In this paper we consider finite lattices given by ordered sets of their meet and…
The set of space-time short-distance structures which can be described through linear operators is limited to a few basic cases. These are continua, lattices and a further short-distance structure which implies an ultraviolet cut-off. Under…
Let $L$ be a slim, planar, semimodular lattice (slim means that it does not contain ${\mathsf M}_3$-sublattices). We call the interval $I = [o, i]$ of $L$ \emph{rectangular}, if there are $u_l, u_r \in [o, i] - \{o,i\}$ such that $o = u_l…
In a totally ordered set the notion of sorting a finite sequence is defined through a suitable permutation of the sequence's indices. In this paper we prove a simple formula that explicitly describes how the elements of a sequence are…