Related papers: Permuting 2-uniform tolerances on lattices
The intrinsic connection between lattice theory and topology is fairly well established, For instance, the collection of open subsets of a topological subspace always forms a distributive lattice. Persistent homology has been one of the…
We study maximal sublattices of finite semidistributive lattices via their complements. We focus on the conjecture that such complements are always intervals, which is known to be true for bounded lattices. Since the class of…
Lattice models with non-hermitian, parity and time-reversal ($\mathcal{PT}$) symmetric Hamiltonians, realized most readily in coupled optical systems, have been intensely studied in the past few years. A $\mathcal{PT}$-symmetric dimer…
This paper establishes some equivalent conditions of a uninorm, extending an arbitrary triangular norm on [0, e] or an arbitrary triangular conorm on [e, 1] to the whole lattice.
A new formulation for fermions on the lattice based on a discretization of a second order formalism is proposed. A comparison with the first order formalism in connection with the $U(1)$ anomaly and the doubling problem is presented. The…
A lattice L is slim if it is finite and the set of its join-irreducible elements contains no three-element antichain. We prove that there exists a positive constant C such that, up to similarity, the number of planar diagrams of these…
In this paper we study prime, maximal and two--class congruences from the point of view of the relationships between them in various kinds of universal algebras, as well as their direct and inverse images through morphisms. This research…
By a 1997 result of R. Freese, an $n$-element lattice has at most $2^{n-1}$ congruences. This motivates us to define the congruence density cd$(L)$ of a finite $n$-element lattice as $|$Con$(L)|/2^{n-1}$, where $|$Con$(L)|$ is the number of…
A singularly perturbed linear system of second order ordinary differential equations of reaction-diffusion type with given boundary conditions is considered. The leading term of each equation is multiplied by a small positive parameter.…
We describe overcommutative varieties of semigroups whose lattice of overcommutative subvarieties satisfies a non-trivial identity or quasiidentity. These two properties turn out to be equivalent.
We propose a family of surface codes with general lattice structures, where the error-tolerances against bit and phase errors can be controlled asymmetrically by changing the underlying lattice geometries. The surface codes on various…
We investigate the complex-temperature singularities of the susceptibility of the 2D Ising model on a square lattice. From an analysis of low-temperature series expansions, we find evidence that as one approaches the point $u=u_s=-1$ (where…
We study non-uniform percolation in a two-dimensional cluster growth model with multiple seeds. With increasing concentration of seeds, the percolation threshold is found to increase monotonically, while the exponents for correlation…
We review the construction of exactly solvable lattice models whose continuum limits are $N=2$ supersymmetric models. Both critical and off-critical models are discussed. The approach we take is to first find lattice models with natural…
To every $n$-dimensional lens space $L$, we associate a congruence lattice $\mathcal L$ in $\mathbb Z^m$, with $n=2m-1$ and we prove a formula relating the multiplicities of Hodge-Laplace eigenvalues on $L$ with the number of lattice…
The set of all transformation monoids on a fixed set of infinite cardinality \lambda, equipped with the order of inclusion, forms a complete algebraic lattice Mon(\lambda) with 2^{\lambda} compact elements. We show that this lattice is…
Following a suggestion due to Bardeen and Pearson, we formulate an effective light-front Hamiltonian for large-N gauge theory in (2+1)-dimensions. Two space-time dimensions are continuous and the remaining space dimension is discretised on…
A discretized massless wave equation in two dimensions, on an appropriately chosen square lattice, exactly reproduces the solutions of the corresponding continuous equations. We show that the reason for this exact solution property is the…
We prove that at all positive temperatures in the bulk of a classical two-dimensional one-component plasma (also called Coulomb or log-gas, or jellium) the variance of the number of particles in large disks grows (strictly) more slowly than…
Multidimensional combinatorial substitutions are rules that replace symbols by finite patterns of symbols in $\mathbb Z^d$. We focus on the case where the patterns are not necessarily rectangular, which requires a specific description of…