Related papers: Simple t-designs: A recursive construction for arb…

One of the main goals of design theory is to classify, characterize and count various combinatorial objects with some prescribed properties. In most cases, however, one quickly encounters a combinatorial explosion and even if the complete…

By suitable examples we illustrate an algorithm for composition of inverse problems.

In this work, we describe a self-replication-based mechanism for designing agents of increasing complexity. We demonstrate the validity of this approach by solving simple, standard evolutionary computation problems in simulation. In the…

We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. We propose a wide class of recursive estimation procedures for the general…

Let $R$ be an associative ring with identity and let $N$ be a nil ideal of $R$. It is shown that units of $R/N$ can be lifted to units in $R$. Under some mild conditions on the ring, a procedure is given to determine those lifted units in a…

We explore a general method based on trees of elementary submodels in order to present highly simplified proofs to numerous results in infinite combinatorics. While countable elementary submodels have been employed in such settings already,…

It is widely known that the recursion operator is a very important component of integrability. It allows one to describe in a compact form both hierarchies of the generalized symmetries and infinite series of the local conservation laws. In…

A relative t-design in the binary Hamming association schemes H(n,2) is equivalent to a weighted regular t-wise balanced design, i.e., certain combinatorial t-design which allow different sizes of blocks and a weight function on blocks. In…

This paper introduces a simple type system for combinatory logic in which combinators have at most one type, whose polymorphism is revealed by application. The combinatory types exactly describe the structure of their values, which may be…

Understanding causality should be a core requirement of any attempt to build real impact through AI. Due to the inherent unobservability of counterfactuals, large randomised trials (RCTs) are the standard for causal inference. But large…

An interval in a combinatorial structure S is a set I of points which relate to every point from S I in the same way. A structure is simple if it has no proper intervals. Every combinatorial structure can be expressed as an inflation of a…

We survey the known results about simple permutations. In particular, we present a number of recent enumerative and structural results pertaining to simple permutations, and show how simple permutations play an important role in the study…

The transition matrix, frequently abbreviated as T-matrix, contains the complete information in a linear approximation of how a spatially localized object scatters an incident field. The T-matrix is used to study the scattering response of…

We present a survey of results concerning the use of inductive constructions to study the rigidity of frameworks. By inductive constructions we mean simple graph moves which can be shown to preserve the rigidity of the corresponding…

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…

We present a method to simplify expressions in the context of an equational theory. The basic ideas and concepts of the method have been presented previously elsewhere but here we tackle the difficult task of making it efficient in…

In this paper, we establish the conditions for some finite abelian groups and the family all the $k$-sets in each of them summing up to an element $x$ to form $t$-designs. We fully characterize the sufficient and necessary conditions for…

In this paper I present a conjecture for a recursive algorithm that finds each permutation of combining two sets of objects (AKA the Shuffle Product). This algorithm provides an efficient way to navigate this problem, as each atomic…

The idea of a co-t-structure is almost "dual" to that of a t-structure, but with some important differences. This note establishes co-t-structure analogues of Beligiannis and Reiten's corresponding results on compactly generated…

This paper proposes new derivations of three well-known sorting algorithms, in their functional formulation. The approach we use is based on three main ingredients: first, the algorithms are derived from a simpler algorithm, i.e. the…