Related papers: Constructing 2-uninorms on bounded lattices by usi…
Pursuing ideas in a recent work of the second author, we determine the isometry classes of unimodular lattices of rank 28, as well as the isometry classes of unimodular lattices of rank 29 without nonzero vectors of norm <=2.
The number of $n$-gaussoids is shown to be a double exponential function in $n$. The necessary bounds are achieved by studying construction methods for gaussoids that rely on prescribing $3$-minors and encoding the resulting combinatorial…
We introduce a general framework to deterministically construct binary measurement matrices for compressed sensing. The proposed matrices are composed of (circulant) permutation submatrix blocks and zero submatrix blocks, thus making their…
The goal of this paper is to unify two lines in a particular area of graph limits. First, we generalize and provide unified treatment of various graph limit concepts by means of a combination of model theory and analysis. Then, as an…
Lattice-free gradient polyhedra can be used to certify optimality for mixed-integer convex minimization models. We consider how to construct these polyhedra for unconstrained models with two integer variables under the assumption that all…
We propose a new generative model for layout generation. We generate layouts in three steps. First, we generate the layout elements as nodes in a layout graph. Second, we compute constraints between layout elements as edges in the layout…
We study symmetry-enriched topological order in two-dimensional tensor network states by using graded matrix product operator algebras to represent symmetry induced domain walls. A close connection to the theory of graded unitary fusion…
This paper presents a novel decoder-based approach for generating manufacturable 3D structures optimized for additive manufacturing. We introduce a deep learning framework that decodes latent representations into geometrically valid,…
We construct all planar semimodular lattices in three simple steps from the direct product of two chains.
This article is the second part of an essay dedicated to lattices freely generated by posets within a variety. The first part dealt with four easy varieties while this part is concerned with finitely generated varieties. Here we present a…
We show that, if L is an extremal Type II lattice of rank 40 or 80, then L is generated by its vectors of norm min(L)+2. This sharpens earlier results of Ozeki, and the second author and Abel, which showed that such lattices L are generated…
The aim of this paper is to construct general forms of ordinary generating functions for special numbers and polynomials involving Fibonacci type numbers and polynomials, Lucas numbers and polynomials, Chebyshev polynomials, Sextet…
In this paper, we present an algorithmic approach to design and construct planar truss structures based on symmetric lattices using modular elements. The method of assembly is similar to Leonardo grids as they both rely on the property of…
In this article, we construct a 2-shaded rigid ${\rm C}^*$ multitensor category with canonical unitary dual functor directly from a standard $\lambda$-lattice. We use the notions of traceless Markov towers and lattices to define the notion…
We give a recursion formula to generate all equivalence classes of biconnected graphs with coefficients given by the inverses of the orders of their groups of automorphisms. We give a linear map to produce a connected graph with say, u,…
There is an established bijection between finite-index subgroups Gamma of Gamma(2) and bipartite graphs on surfaces, or, equivalently, certain triples of permutations. We utilize this relationship to study both congruence and noncongruence…
The standard unitarity-cut method is applied to several massive two-dimensional models, including the world-sheet AdS$_5\times S^5$ superstring, to compute $2\to 2$ scattering S-matrices at one loop from tree level amplitudes. Evidence is…
We consider the problem of finding lower bounds on the number of unlabeled $n$-element lattices in some lattice family. We show that if the family is closed under vertical sum, exponential lower bounds can be obtained from vertical sums of…
In this paper, we count acyclic and strongly connected uniform directed labeled hypergraphs. For these combinatorial structures, we introduce a specific generating function allowing us to recover and generalize some results on the number of…
The unextendible orthogonal matrices (UPBs) can be used for various problems in quantum information. We provide an algorithm to check if two UPBs are non-equivalent to each other. We give a method to construct UPBs and we apply this method…