Related papers: Constructions and uses of incomplete pairwise bala…

This paper gives a construction of group divisible designs on the binary extension fields with block sizes 3, 4, 5, 6, and 7, respectively, which is motivated from the decoding of binary quadratic residue codes. A conjecture is proposed for…

Building on coprincipal mesoprimary decomposition [Kahle and Miller, 2014], we combinatorially construct an irreducible decomposition of any given binomial ideal. In a parallel manner, for congruences in commutative monoids we construct…

Mining groups of genes that consistently co-express is an important problem in biomedical research, where it is critical for applications such as drug-repositioning and designing new disease treatments. Recently, Cooley et al. modeled this…

Motivated by Tverberg-type problems in topological combinatorics and by classical results about embeddings (maps without double points), we study the question whether a finite simplicial complex K can be mapped into R^d without…

A $3$-$(v,\{4,6\},1)$ design is a configuration of $v$ points and a collection of $4$- and $6$-element subsets called blocks, that jointly contain every 3-element subset exactly once. Using an exhaustive computer search on $v\leq 28$ points…

We use difference sets to construct interesting sets of lines in complex space. Using (v,k,1)-difference sets, we obtain k^2-k+1 equiangular lines in C^k when k-1 is a prime power. Using semiregular relative difference sets with parameters…

Designing complex engineered systems requires managing tightly coupled trade-offs between subsystem capabilities and resource requirements. Monotone co-design provides a compositional language for such problems, but its generality does not…

We consider two basic algorithmic problems concerning tuples of (skew-)symmetric matrices. The first problem asks to decide, given two tuples of (skew-)symmetric matrices $(B_1, \dots, B_m)$ and $(C_1, \dots, C_m)$, whether there exists an…

We address the question of constructing explicitly quasi-uniform codes from groups. We determine the size of the codebook, the alphabet and the minimum distance as a function of the corresponding group, both for abelian and some nonabelian…

In a mass partition problem, we are interested in finding equitable partitions of smooth measures in $\mathbb{R}^d$. In this manuscript, we study the problem of finding simultaneous bisections of measures using scaled copies of a prescribed…

The method of constructing approximate solutions of the first boundary value problem for linear differential equations based on incomplete (even and odd) trigonometric splines is considered. The theoretical positions are illustrated by…

Unitary designs are essential tools in several quantum information protocols. Similarly to other design concepts, unitary designs are mainly used to facilitate averaging over a relevant space, in this case, the unitary group…

We study edge-isoperimetric inequalities in chamber graphs of affine hyperplane arrangements. Our approach is topological: to a set of chambers we associate its thickening in Euclidean space and estimate its edge boundary through the…

For a fixed integer $k$, we consider the set of noncrossing partitions, where both the block sizes and the difference between adjacent elements in a block is $1\bmod k$. We show that these $k$-indivisible noncrossing partitions can be…

It is well known that Space-Time Block Codes (STBCs) from orthogonal designs (ODs) are single-symbol decodable/symbol-by-symbol decodable (SSD) and are obtainable from unitary matrix representations of Clifford algebras. However, SSD codes…

Let $\Psi(t,k)$ denote the set of pairs $(v,\lambda)$ for which there exists a graphical $t$-$(v,k,\lambda)$ design. Most results on graphical designs have gone to show the finiteness of $\Psi(t,k)$ when $t$ and $k$ satisfy certain…

In this paper, using group actions, we introduce a new method for constructing partial geometric designs (sometimes referred to as $1\frac{1}{2}$-designs). Using this new method, we construct several infinite families of partial geometric…

The intersection problem for additive (extended and non-extended) perfect codes, i.e. which are the possibilities for the number of codewords in the intersection of two additive codes C1 and C2 of the same length, is investigated. Lower and…

Data collection is a critical step in statistical inference and data science, and the goal of statistical experimental design (ED) is to find the data collection setup that can provide most information for the inference. In this work we…

We provide a new construction for a set of boxes approximating axis-parallel boxes of fixed volume in $[0, 1]^d$. This improves upper bounds for the minimal dispersion of a point set in the unit cube and its inverse in both the periodic and…