Related papers: Permuting 2-uniform tolerances on lattices
It is shown that an n-dimensional unimodular lattice has minimal norm at most 2[n/24] +2, unless n = 23 when the bound must be increased by 1. This result was previously known only for even unimodular lattices. Quebbemann had extended the…
A switching method is a graph operation that results in cospectral graphs (graphs with the same spectrum). Work by Wang and Xu [Discrete Math. 310 (2010)] suggests that most cospectral graphs with cospectral complements can be constructed…
We examine the link approach to constructing a lattice theory of N=2 super Yang Mills theory in two dimensions. The goal of this construction is to provide a discretization of the continuum theory which preserves all supersymmetries at…
We propose a new formulation which realizes exact twisted supersymmetry for all the supercharges on a lattice by twisted superspace formalism. We show explicit examples of N=2 twisted supersymmetry invariant BF and Wess-Zumino models in two…
We enumerate over even characteristic the components of the permutation module of the symmetric group of even degree acting on the set of its fixed point free involutions. We find the vertex and Brauer quotient for each component, and the…
Let $a,b$ be elements in a unital C$^*$-algebra with $0\leq a,b\leq 1$. The element $a$ is absolutely compatible with $b$ if $$\vert a - b \vert + \vert 1 - a - b \vert = 1.$$ In this note, we describe a complete list of absolutely…
A simplified test of universality in Lattice QCD is performed by analytically evaluating the continuous Euclidean time limits of various lattice fermion determinants, both with and without a Wilson term to lift the fermion doubling on the…
A unified classification and analysis is presented of two dimensional Dirac operators of QCD-like theories in the continuum as well as in a naive lattice discretization. Thereby we consider the quenched theory in the strong coupling limit.…
Let L denote the variety of lattices. In 1982, the second author proved that L is strongly tolerance factorable, that is, the members of L have quotients in L modulo tolerances, although L has proper tolerances. We did not know any other…
We prove a remarkable combinatorial symmetry in the number of spanning configurations in site percolation: for a large class of lattices, the number of spanning configurations with an odd or even number of occupied sites differs by $\pm 1$.…
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.
We consider a special class of two-dimensional discrete equations defined by relations on elementary NxN squares, N>2, of the square lattice Z^2, and propose a new type of consistency conditions on cubic lattices for such discrete equations…
Let $\Gamma$ be a finite, undirected, connected, simple graph. We say that a matching $\mathcal{M}$ is a \textit{permutable $m$-matching} if $\mathcal{M}$ contains $m$ edges and the subgroup of $\text{Aut}(\Gamma)$ that fixes the matching…
We survey results concerning special elements of nine types (modular, lower-modular, upper-modular, cancellable, distributive, codistributive, standard, costandard and neutral elements) in the lattice of all semigroup varieties and certain…
We formulate ${\cal N} = 2^*$ supersymmetric Yang-Mills theory on a Euclidean spacetime lattice using the method of topological twisting. The lattice formulation preserves one scalar supersymmetry charge at finite lattice spacing. The…
We consider tolerances $T$ compatible with an equivalence $E$ on $U$, meaning that the relational product $E \circ T$ is included in $T$. We present the essential properties of $E$-compatible tolerances and study rough approximations…
Let the finite distributive lattice $D$ be isomorphic to the congruence lattice of a finite lattice $L$. Let $Q$ denote those elements of $D$ that correspond to principal congruences under this isomorphism. Then $Q$ contains $0,1 \in D$ and…
Following on from a general observation in an earlier paper, we consider the continuous symmetries of a certain class of conformal field theories constructed from lattices and their reflection-twisted orbifolds. It is shown that the naive…
We construct two-dimensional ${\cal N} = (2, 2)$ supersymmetric gauge theories on a Euclidean spacetime lattice with matter in the two-index symmetric and anti-symmetric representations of SU($N_c$) color group. These lattice theories…
We prove the density hypothesis for congruence subgroups of an irreducible uniform lattice in $\mathrm{PSL}_2(\mathbb{R})^d$, extending previous results on the spherical density hypothesis to bound multiplicities of non-tempered…