相关论文: The On-Line Encyclopedia of Integer Sequences
We provide a description of the Epidemics on Networks (EoN) python package designed for studying disease spread in static networks. The package consists of over $100$ methods available for users to perform stochastic simulation of a range…
Biological sequences do not come at random. Instead, they appear with particular frequencies that reflect properties of the associated system or phenomenon. Knowing how biological sequences are distributed in sequence space is thus a…
This paper presents combinatorial facts dealing with the number of unlabeled partially ordered sets (posets) refined by the number of arcs in the Hasse diagram (sequence A342447 in OEIS). The main result is that the differences with respect…
We present a subjective selection of methods for complex systems analysis ranging from statistical tools through numerical methods based on AI to both linear and non-linear ODEs and PDEs. All the notions apply the network structure and are…
The ``comma sequence'' starts with 1 and is defined by the property that if k and k' are consecutive terms, the two-digit number formed from the last digit of k and the first digit of k' is equal to the difference k'-k. If there is more…
An integer linear system (ILS) is a linear system with integer constraints. The solution graph of an ILS is defined as an undirected graph defined on the set of feasible solutions to the ILS. A pair of feasible solutions is connected by an…
Inversion sequences are integer sequences $(\sigma_1, \dots, \sigma_n)$ such that $0 \leqslant \sigma_i < i$ for all $1 \leqslant i \leqslant n$. The study of pattern-avoiding inversion sequences began in two independent articles by…
A zero-sum sequence of integers is a sequence of nonzero terms that sum to 0. Let $k>0$ be an integer and let $[-k,k]$ denote the set of all nonzero integers between $-k$ and $k$. Let $\ell(k)$ be the smallest integer $\ell$ such that any…
Understanding human's language requires complex world knowledge. However, existing large-scale knowledge graphs mainly focus on knowledge about entities while ignoring knowledge about activities, states, or events, which are used to…
The present work is dedicated to searching parameters, alternative to entropy, applicable for description of highly organized systems. The general concept has been offered, in which the system complexity and order are functions of the order…
Sequence diagrams are a popular technique for describing interactions between software entities. However, because the OMG group's UML standard is not based on a rigorous mathematical structure, it is impossible to deduce a single…
Based on Euclid's algorithm, we find a kind of special sequences which play an interesting role in the study of primes. We call them W Sequences. They not only ties up the distribution of primes in short interval but also enables us to give…
This paper deals with algorithms for producing and ordering lexical and nonlexical sequences of a given degree. The notion of "elementary operations" on positive integral sequences is introduced. Our main theorem answers the question of…
This manuscript is a tutorial on tig sequences that emerged after the name "contig", and are of diverse purposes in sequence bioinformatics. We review these different sequences (unitigs, simplitigs, monotigs, omnitigs to cite a few), give…
Inversion sequences of length $n$ are integer sequences $e_1,\ldots ,e_n$ with $0\le e_i<i$ for all $i$, which are in bijection with the permutations of length $n$. In this paper, we classify all Wilf equivalence classes of pattern-avoiding…
We prove that five ways to define entry A086377 in the On-Line Encyclopedia of Integer Sequences do lead to the same integer sequence.
A parameterized algebraic theory of instruction sequences, objects that represent the behaviours produced by instruction sequences under execution, and objects that represent the behaviours exhibited by the components of the execution…
In a \emph{weighted sequence}, for every position of the sequence and every letter of the alphabet a probability of occurrence of this letter at this position is specified. Weighted sequences are commonly used to represent imprecise or…
We explore a question related to the celebrated Erd\H{o}s-Szekeres Theorem and develop a geometric approach to answer it. Our main object of study is the Erd\H{o}s-Szekeres tableau, or EST, of a number sequence. An EST is the sequence of…
In this paper we formally define the family of sequences know as "Pea Pattern". We then analyse its behaviour and conditions for fixed and periodic points. The paper ends with a list of fixed points and cycles.