Related papers: Strongly modular lattices with long shadow
Categorical skew lattices are a variety of skew lattices on which the natural partial order is especially well behaved. While most skew lattices of interest are categorical, not all are. They are characterized by a countable family of…
We demonstrate that there is a large class of compact metric spaces for which the shadowing property can be characterized as a structural property of the space of dynamical systems. We also demonstrate for this class of spaces, that in…
In a recent paper, G. Cz\'edli and E.\,T. Schmidt present a structure theorem for planar semimodular lattices. In this note, we present an alternative proof.
We prove several fundamental results about divisorial integral domains in the setup of multiplicative lattices.
We construct bases for the spaces of higher order modular forms of all orders and weights. We also provide a cohomological interpretation of these forms.
We analyse various structural and order-theoretical aspects of abstract separation systems and partial lattices, as well as the relationship between the different submodularity conditions one can impose on them.
Strong gravitational lensing is a promising probe of the substructure of dark matter halos. Deep learning methods have the potential to accurately identify images containing substructure, and differentiate WIMP dark matter from other well…
We characterize the finite intervals of the Muchnik lattice by proving that they are a certain proper subclass of the finite distributive lattices.
The Finiteness Problem is shown to be unsolvable for any sufficiently large class of modular lattices.
Characteristic Lie rings for Toda type 2+1 dimensional lattices are defined. Some properties of these rings are studied. Infinite sequence of special kind modules are introduced. It is proved that for known integrable lattices these modules…
For many equation-theoretical questions about modular lattices, Hall and Dilworth give a useful construction: Let $L_0$ be a lattice with largest element $u_0$, $L_1$ be a lattice disjoint from $L_0$ with smallest element $v_1$, and $a \in…
We construct all planar semimodular lattices in three simple steps from the direct product of two chains.
In this work we develop some categorical aspects of the double structure of a module.
We characterize all the strongly monotypic polytopes. Hadwiger's conjecture for this class of polytopes is deduced from the characterization.
We classify strongly homotopy Lie algebras - also called L-infinity algebras - of one even and two odd dimensions, which are related to $2|1$-dimensional $Z_2$-graded Lie algebras. What makes this case interesting is that there are many…
Several collaborations have recently performed lattice calculations aimed specifically at dark matter, including work with SU(2), SU(3), SU(4) and SO(4) gauge theories to represent the dark sector. Highlights of these studies are presented…
The extremal 3-modular lattice $[\pm G_2(3)]_{14}$ with automorphism group $C_2 \times G_2(\F_3) $ is the unique dual strongly perfect lattice of dimension 14.
We characterize when a finite lattice is distributive by the existences of some particular classes of Koszul filtrations.
We translate notions and results of decomposition and dimension theories for module categories, into the lattice environment. In particular we translate dimension theory in module categories to complete modular upper-continuous lattices.
We introduce special classes of irreducible representations of groups: thick representations and dense representations. Denseness implies thickness, and thickness implies irreducibility. We show that absolute thickness and absolute…