Related papers: A note on construction of the Leech lattice
In this paper we discuss and characterize several set-theoretic solutions of the Yang-Baxter equation obtained using skew lattices, an algebraic structure that has not yet been related to the Yang-Baxter equation. Such solutions are…
We present an easy construction producing a Kleene lattice K from an arbitrary distributive lattice L and a non-empty subset of L. We show that L can be embedded into K and compute the cardinality of K under certain additional assumptions.…
The aim of this note is to share the observation that the set of elementary operations of Turing on lattice knots can be reduced to just one type of simple local switches.
In a recent preprint, Lai and Rohatgi compute the generating functions of lozenge tilings of "quartered hexagons with dents" by applying the method of "graphical condensation". The purpose of this note is to exhibit how (a generalization…
A practical method for constructing a nontrivial homomorphsim between Verma modules is described.
Questions that seek to determine whether a hyperplane arrangement property, be it geometric, arithmetic or topological, is of a combinatorial nature (that is determined by the intersection lattice) are abundant in the literature. To tackle…
We give a new proof of Chen-Lin result with Li-Zhang method.
We construct an even extremal lattice of rank 64 by means of a generalized quadratic residue code.
In this paper, constructions of multimagic squares are investigated. Diagonal Latin squares and Kronecker products are used to get some constructions of multimagic squares. Consequently, some new families of compound multimagic squares are…
We prove that a tolerance relation of a lattice is a homomorphic image of a congruence relation.
A method is presented for calculating the Lie point symmetries of a scalar difference equation on a two-dimensional lattice. The symmetry transformations act on the equations and on the lattice. They take solutions into solutions and can be…
We present a method to produce examples of non-homeomorphic conjugate complex varieties based on the genus theory of lattices. As an application, we give examples of arithmetic Zariski pairs.
We present some new lower bound estimates for certain numbers in Laver table theory and introduce several related structures of interest.
A method is proposed for latticizing a class of supersymmetric gauge theories, including N=4 super Yang-Mills. The technique is inspired by recent work on ``deconstruction''. Part of the target theory's supersymmetry is realized exactly on…
We introduce a concept of multiplicity lattices of 2-multiarrangements, determine the combinatorics and geometry of that lattice, and give a criterion and method to construct a basis for derivation modules effectively.
The architecture and capabilities of the computers currently in use for large-scale lattice QCD calculations are described and compared. Based on this present experience, possible future directions are discussed.
I present here another example of a lattice fibration, a discrete version of the highest dimensional Hopf fibration: $S^{7}\longrightarrow S^{15} \longrightarrow S^{8}$.
These are notes for a very rapid introduction to the basics of exterior differential systems and their connection with what is now known as Lie theory, together with some typical and not-so-typical applications to illustrate their use.
Lattice results in supersymmetry are summarized. Past, present and future perspectives are discussed.
In this paper we propose a new approach to formulate the field theory on a lattice. This approach can eliminate the Fermion doubling problem, preserve the chiral symmetry and get the same dispersion relation for both Fermion and Boson…