Related papers: Chain lengths in the type $B$ Tamari lattice
We describe a method to put chiral gauge theories on the lattice. Our method makes heavy use of the effective action for chiral fermions in the continuum, which is in general complex. As an example we discuss the chiral Schwinger model.
For a certain class of two-dimensional lattices, lattice-dual pairs are shown to have the same bond percolation critical exponents. A computational proof is given for the martini lattice and its dual to illustrate the method. The result is…
We discuss a general framework for the realization of a family of abelian lattice gauge theories, i.e., link models or gauge magnets, in optical lattices. We analyze the properties of these models that make them suitable to quantum…
We solve a recent question of Caro, Patk\'os and Tuza by determining the exact maximum number of edges in a bipartite connected graph as a function of the longest path it contains as a subgraph and of the number of vertices in each side of…
Twisted torus knots and links are given by twisting adjacent strands of a torus link. They are geometrically simple and contain many examples of the smallest volume hyperbolic knots. Many are also Lorenz links. We study the geometry of…
This paper treats certain integral lattices with respect to ternary quadratic forms, which are obtained from the data of a non-zero element and a maximal lattice in a quaternary quadratic space. Such a lattice can be described by means of…
We define the pattern fragment for higher-order unification problems in linear and affine type theory and give a deterministic unification algorithm that computes most general unifiers.
We establish a connection between the algebraic geometry of the type B permutohedral toric variety and the combinatorics of delta-matroids. Using this connection, we compute the volume and lattice point counts of type B generalized…
I discuss a new approach to constructing lattices for gauge theories with extended supersymmetry. The lattice theories themselves respect certain supersymmetries, which in many cases allows the target theory to be obtained in the continuum…
We continue the study of the B-Toda hierarchy (the Toda lattice with the constraint of type B) which can be regarded as a discretization of the BKP hierarchy. We introduce the tau-function of the B-Toda hierarchy and obtain the bilinear…
This paper studies the structure of Lax pairs associated with integrable lattice systems (where space is a one-dimensional lattice, and time is continuous). It describes a procedure for generating examples of such systems, and emphasizes…
In the standard approach to lattice proteins the models based on nearest neighbor interaction are used. In this kind of models it is difficult to explain the existence of secondary structures --- special preferred conformations of protein…
We construct a sequence of lattices $\{L_{n_i}\subset \mathbb R^{n_i}\}$ for $n_i\longrightarrow\infty$, with exponentially large kissing numbers, namely, $\log_2\tau(L_{n_i})> 0.0338\cdot n_i -o(n_i)$. We also show that the maximum lattice…
In state-of-the-art optical lattice clocks, beyond-electric-dipole polarizability terms lead to a break-down of magic wavelength trapping. In this Letter, we report a novel approach to evaluate lattice light shifts, specifically addressing…
We introduce a new combinatorial structure: the metasylvester lattice on decreasing trees. It appears in the context of the $m$-Tamari lattices and other related $m$-generalizations. The metasylvester congruence has been recently introduced…
Discussions are made on the structures of chirally invariant lattice actions without any restriction of hermiticity. With the help of the Ward-Takahashi identity a general conclusion can be derived that there must be species doublers in any…
In this paper, we investigate a general method to establish tame and norm relations for special cycles in Shimura varieties, using unitary cycles in odd orthogonal Shimura varieties as a guiding example.
We analyze the problem of discovering long cycles inside a graph. We propose and test two algorithms for this task. The first one is based on recent advances in statistical mechanics and relies on a message passing procedure. The second…
Following a recent suggestion by Nielsen, Rugh, and Rugh, we study the energy scaling of the maximal Lyapunov exponent of classical Hamiltonian SU(2) lattice gauge theory. It is shown that the conjectured scaling behavior $\lambda_0\sim…
A brief introduction to the theory of ordered sets and lattice theory is given. To illustrate proof techniques in the theory of ordered sets, a generalization of a conjecture of Daykin and Daykin, concerning the structure of posets that can…