Related papers: Mockingbird lattices
We utilize degenerate perturbation theory to investigate continuous-time quantum search on second-order truncated simplex lattices. In this work, we show that the construction of the Hamiltonian must consider the structure of the lattice.…
Moir\'e effects in twisted or lattice-incommensurate vertical assemblies of two-dimensional crystals give rise to a new class of quantum materials with rich transport and optical phenomena, including correlated electron physics in flat…
For a finite lattice L, the congruence lattice Con L of L can be easily computed from the partially ordered set J(L) of join-irreducible elements of L and the join-dependency relation D\_L on J(L). We establish a similar version of this…
The character theory of finite groups has numerous basic questions that are often already quite involved: enumerating of irreducible characters, their character formulas, point-wise product decompositions, and restriction/induction between…
This paper has been withdrawn by the authors due to a crucial computational error. In this paper we deal with the finite case. We prove that a finite bounded ordered set can be represented as the order of principal congruences of a finite…
Laplante-Anfossi associated to each rooted plane tree a polytope called an operahedron. He also defined a partial order on the vertex set of an operahedron and asked if the resulting poset is a lattice. We answer this question in the…
Gr\"atzer asked in 1971 for a characterization of sublattices of Tamari lattices (associahedra). A natural candidate was coined by McKenzie in 1972 with the notion of a bounded homomorphic image of a free lattice---in short, bounded…
We investigate the Hubbard Hamiltonian on ladders where the number of sites per rung alternates between two and three. These geometries are bipartite, with a non-equal number of sites on the two sublattices. Thus they share a key feature of…
We introduce and characterize various gluing constructions for residuated lattices that intersect on a common subreduct, and which are subalgebras, or appropriate subreducts, of the resulting structure. Starting from the 1-sum construction…
In this paper we discuss the properties of the biordered set obtained from a complemented modular lattice and defines an operation using the sandwich elements of the biordered set. Further we describe a biordered subset satisfying certain…
A consistent guiding-center Hamiltonian theory is derived by Lie-transform perturbation method, with terms up to second order in magnetic-field nonuniformity. Consistency is demonstrated by showing that the guiding-center transformation…
We resolve a question of Gillespie, Griffin, and Levinson that asks for a combinatorial bijection between two classes of trivalent trees, tournament trees and slide trees, that both naturally arise in the intersection theory of the moduli…
A modular or distributive lattice is `diamond-colored' if its order diagram edges are colored in such a way that, within any diamond of edges, parallel edges have the same color. Such lattices arise naturally in combinatorial representation…
Given a nonnegative integer $m$ and a finite collection ${\mathcal A}$ of linear forms on ${\mathbb Q}^d$, the arrangement of affine hyperplanes in ${\mathbb Q}^d$ defined by the equations $\alpha(x) = k$ for $\alpha \in {\mathcal A}$ and…
The first two Hamiltonian structures and the recursion operator connecting all evolution systems and Hamiltonian structures of the N=2 supersymmetric (n,m)-GNLS hierarchy are constructed in terms of N=2 superfields in two different…
Neighborhood regression has been a successful approach in graphical and structural equation modeling, with applications to learning undirected and directed graphical models. We extend these ideas by defining and studying an algebraic…
A lattice is a partially-ordered set in which every pair of elements has a unique meet (greatest lower bound) and join (least upper bound). We present new data structures for lattices that are simple, efficient, and nearly optimal in terms…
We study the Whitney numbers of the first kind of combinatorial geometries. The first part of the paper is devoted to general results relating the M\"{o}bius functions of nested atomistic lattices, extending some classical theorems in…
We investigate a construction of an integral residuated lattice starting from an integral residuated lattice and two sets with an injective mapping from one set into the second one. The resulting algebra has a shape of a Chinese cascade…
We survey systematic approaches to basis-restricted fragments of propositional logic and modal logics, with an emphasis on how expressive power and computational complexity depend on the allowed operators. The propositional case is…