Related papers: An Exceptional Combinatorial Sequence and Standard…
The dynamical system generated by the iterated calculation of the high order gaps between neighboring terms of a sequence of natural numbers is remarkable and only incidentally characterized at the boundary by the notable Proth-Glibreath…
Set partitions and permutations with restrictions on the size of the blocks and cycles are important combinatorial sequences. Counting these objects lead to the sequences generalizing the classical Stirling and Bell numbers. The main focus…
The computational cost of micromechanics for heterogeneous materials can be reduced in certain cases where symmetric boundary conditions are applicable. We derived an eighth symmetric formulation of the Generalized Method of Cells for…
This paper studies nested sequents for quantified modal logics. In particular, it considers extensions of the propositional modal logics definable by the axioms D, T, B, 4, and 5 with varying, increasing, decreasing, and constant domains.…
A typical system of k difference (or differential) equations can be compressed, or folded into a difference (or ordinary differential) equation of order k. Such foldings appear in control theory as the canonical forms of the controllability…
We consider consistent particle systems, which include independent random walkers, the symmetric exclusion and inclusion processes, as well as the dual of the KMP model. Consistent systems are such that the distribution obtained by first…
Separation systems are posets with additional structure that form an abstract setting in which tangle-like clusters in graphs, matroids and other combinatorial structures can be expressed and studied. This paper offers some basic theory…
In this paper, we study decoupled mixed element schemes for fourth order problems. A general process is designed such that an elliptic problem on high-regularity space is transformed to a decoupled system with spaces of low order involved…
Recollements of triangulated categories may be seen as exact sequences of such categories. Iterated recollements of triangulated categories are analogues of geometric or topological stratifications and of composition series of algebraic…
Semiconstrained systems were recently suggested as a generalization of constrained systems, commonly used in communication and data-storage applications that require certain offending subsequences be avoided. In an attempt to apply…
Sequence-based modeling broadly refers to algorithms that act on data that is represented as an ordered set of input elements. In particular, Machine Learning algorithms with sequences as inputs have seen successfull applications to…
A partial Steiner triple system is is $sequenceable$ if the points can be sequenced so that no proper segment can be partitioned into blocks. We show that, if $0 \leq a \leq (n-1)/3$, then there exists a nonsequenceable PSTS$(n)$ of size…
We study an abstract notion of tree structure which lies at the common core of various tree-like discrete structures commonly used in combinatorics: trees in graphs, order trees, nested subsets of a set, tree-decompositions of graphs and…
For itinerant fermionic and bosonic systems, we study `particle entanglement', defined as the entanglement between two subsets of particles making up the system. We formulate the general structure of particle entanglement in many-fermion…
We produce a long exact sequence whose terms are unit groups of associative algebras that behave as inner automorphisms of a given tensor. Our sequence generalizes known sequences for associative and non-associative algebras. In a manner…
Irreversible aggregation is revisited in view of recent work on renormalization of complex networks. Its scaling laws and phase transitions are related to percolation transitions seen in the latter. We illustrate our points by giving the…
New sets (typically found by computer search) with Sidon constant equal to the square root of their cardinalities are given. For each integer $N$ there are only a finite number of groups of prime order containing $N$-element extreme sets.…
We investigate the existence and the properties of fully separable (fully factorized) ground states in quantum spin systems. Exploiting techniques of quantum information and entanglement theory we extend a recently introduced method and…
We study the structures of arbitrary split Leibniz triple systems. By developing techniques of connections of roots for this kind of triple systems, under certain conditions, in the case of $T$ being of maximal length, the simplicity of the…
The work in this article is concerned with two different types of families of finite sets: separating families and splitting families (they are also called "systems"). These families have applications in combinatorial search, coding theory,…