Related papers: Some results on the Ryser design conjecture-II
The theory of designs is an important branch of combinatorial mathematics. It is well-known in the theory of designs that a finite subset of a sphere is a tight spherical 1-design if and only if it is a pair of antipodal points. On the…
In this paper we study a certain generalization of combinatorial designs related to almost difference sets, namely the $t$-adesign, which was coined by Cunsheng Ding in 2015. It is clear that $2$-adesigns are a kind of partially balanced…
The rational design of novel polymers with tailored material properties has been a long-standing challenge in the field due to the large number of possible polymer design variables. To accelerate this design process, there is a critical…
A design is $G$-additive with $G$ an abelian group, if its points are in $G$ and each block is zero-sum in $G$. All the few known ``manageable" additive Steiner 2-designs are $\mathrm{EA}(q)$-additive for a suitable $q$, where…
Motivated by the study of reversal behaviour of myxobacteria, in this article we are interested in a kinetic model for reversal dynamics, in which particles with directions close to be opposite undergo binary collision resulting in…
Two, replica symmetry breaking specific, quantities of the Ising spin glass --- the breakpoint x1 of the order parameter function and the Almeida-Thouless line --- are calculated in six dimensions (the upper critical dimension of the…
Randomized higher-order computation can be seen as being captured by a lambda calculus endowed with a single algebraic operation, namely a construct for binary probabilistic choice. What matters about such computations is the probability of…
We prove the existence of maximal (and minimal) solution for one-dimensional generalized doubly reflected backward stochastic differential equation (RBSDE for short) with irregular barriers and stochastic quadratic growth, for which the…
Over the past decade, characterizing the exact asymptotic risk of regularized estimators in high-dimensional regression has emerged as a popular line of work. This literature considers the proportional asymptotics framework, where the…
The obvious way to construct a GDD (group-divisible design) recursively is to use Wilson's Fundamental Construction for GDDs (WFC). Then a PBD (pairwise balanced design) is often obtained by adding a new point to each group of the GDD.…
We study two kinds of generalizations of symmetric block designs to higher dimensions, the so-called $\mathcal{C}$-cubes and $\mathcal{P}$-cubes. For small parameters, all examples up to equivalence are determined by computer calculations.…
We prove three theorems giving extremal bounds on the incidence structures determined by subsets of the points and blocks of a balanced incomplete block design (BIBD). These results generalize and strengthen known bounds on the number of…
In this work, we propose an optimization approach for constructing various classes of circulant combinatorial designs that can be defined in terms of autocorrelations. The problem is formulated as a so-called feasibility problem having…
A construction described by the current author in 2017 uses two linear `prototype' graphs to build a compound graph with Ramsey properties inherited from the prototypes. This paper describes a generalisation of that construction which has…
The combinatorial theory of rotor-routers has connections with problems of statistical mechanics, graph theory, chaos theory, and computer science. A rotor-router network defines a deterministic walk on a digraph G in which a particle walks…
A design is a collection of distinct points in a given set $X$, which is assumed to be a compact subset of $R^d$, and the mesh-ratio of a design is the ratio of its fill distance to its separation radius. The uniformity constant of a…
Modern experimental methods enable the creation of self-assembly building blocks with tunable interactions, but optimally exploiting this tunability for the self-assembly of desired structures remains an important challenge. Many studies of…
We discuss, and give examples of, methods for randomly implementing some minimax robust designs from the literature. These have the advantage, over their deterministic counterparts, of having bounded maximum loss in large and very rich…
The Alperin--McKay conjecture relates irreducible characters of a block of an arbitrary finite group to those of its $p$-local subgroups. A refinement of this conjecture was stated by the author in a previous paper. We prove that this…
A $biased\ graph$ is a pair $(G,\mathcal{B})$, where $G$ is a graph and $\mathcal{B}$ is a collection of `balanced' circuits of $G$ such that no $\Theta$-subgraph of $G$ contains precisely two balanced circuits. We prove a Ramsey-type…