Related papers: Chain lengths in the type $B$ Tamari lattice
For a many-to-many matching market, we study the lattice structure of the set of random stable matchings. We define a partial order on the random stable set and present two intuitive binary operations to compute the least upper bound and…
We derive a formula for the number of lattice points in type B generalized permutohedra, providing a concise alternative to the formula obtained recently by Eur, Fink, Larson, and Spink as a result from a study of delta-matroids. Our…
In this paper we study maximal chains in certain lattices constructed from powers of chains by iterated lax colimits in the $2$-category of posets. Such a study is motivated by the fact that in lower dimensions, we get some familiar…
We construct lattice actions for a variety of (2,2) supersymmetric gauge theories in two dimensions with matter fields interacting via a superpotential.
In this paper, we define two kinds of hook length for internal vertices of complete $m$-ary trees, and deduce their corresponding hook length formulas, which generalize the main results obtained by Du and Liu.
I review the ongoing attempts to define chiral gauge theories using the lattice regularization.
The duality between a class of the Davey-Stewartson type coupled systems and a class of two-dimensional Toda type lattices is discussed. For the recently found integrable lattice the hierarchy of symmetries is described. Second and third…
The canonical extension of a lattice is in an essential way a two-sided completion. Domain theory, on the contrary, is primarily concerned with one-sided completeness. In this paper, we show two things. Firstly, that the canonical extension…
We report on a calculation of the $B^*B\pi$ coupling in lattice QCD. The strong matrix element $\langle B \pi | B^*\rangle$ is directly related to the leading order low-energy constant in heavy meson chiral perturbation theory (HM$\chi$PT)…
We introduce a new type of lattice path, called brick-wall lattice path, and we derive a formula which counts the number of paths on these lattices imposing certain restrictions on the Cartesian plane. Connections to the Fibonacci sequence,…
A lattice $\Lambda$ is said to be an extension of a sublattice $L$ of smaller rank if $L$ is equal to the intersection of $\Lambda$ with the subspace spanned by $L$. The goal of this paper is to initiate a systematic study of the geometry…
Multiple gaps in the tight-binding band of a pentagonal lattice are found. Unlike the Cairo pentagonal lattice this lattice is made of irregular pentagons with arms of different lengths. The tight-binding Hamiltonian is exactly solved to…
Two structures are said to be equimorphic if each embeds in the other. Such structures cannot be expected to be isomorphic, and in this paper we investigate the special case of linear orders, here also called chains. In particular we…
In this paper, we define a property, trimness, for lattices. Trimness is a not-necessarily-graded generalization of distributivity; in particular, if a lattice is trim and graded, it is distributive. Trimness is preserved under taking…
For two decades it was believed that chiral symmetries cannot be realized in lattice field theory but this has changed now. Highlights of these new developments will be presented with emphasis on the mathematical structure of the so called…
Bobbin lace is a fibre art form in which intricate and delicate patterns are created by braiding together many threads. An overview of how bobbin lace is made is presented and illustrated with a simple, traditional bookmark design. Research…
In classical physics, calculating the slack of a hanging chain is a problem that has attracted interest. This study aims to solve this problem through experiment and theory. When the length and distance of both the ends of a hanging chain…
We give classifications of integral lattices which include the Barnes-Wall lattice $BW_{16}$ or laminated lattices of dimension $1 \leqslant d \leqslant 8$ and of minimum 4. Also, we give certain lattice neighboring from each lattice.…
We obtain lower bound for the maximum distance between any three distinct points in an affine lattice which are close to a helix with small curvature and torsion.
Within the overlap framework, I derive the main formulae one finds today in papers touting a ``new approach'' to the regularization of chiral gauge theories. My main objective is to clear up an unhealthy confusion about how many successful…