Related papers: IPr* recurrence and nilsystems
Recurrence properties of systems and associated sets of integers that suffice for recurrence are classical objects in topological dynamics. We describe relations between recurrence in different sorts of systems, study ways to formulate…
In this paper we obtained several properties that the characteristic polynomials of the unit-primitive matrix satisfy. In addition, using these properties we have shown that the recurrence relation given as in the formula (1) is true. In…
We survey and prove properties a family of recurrences bears in relation to integer representations, compositions, the Pascal triangle, sums of digits, Nim games and Beatty sequences.
A nilspace system is a generalization of a nilsystem, consisting of a compact nilspace X equipped with a group of nilspace translations acting on X. Nilspace systems appear in different guises in several recent works, and this motivates the…
We generalize the IP-polynomial Szemer\'edi theorem due to Bergelson and McCutcheon and the nilpotent Szemer\'edi theorem due to Leibman. Important tools in our proof include a generalization of Leibman's result that polynomial mappings…
We present some Euler-type recurrences for the partition function $p(n)$.
We provide a nilpotency criterion for fusion systems in terms of the vanishing of its cohomology with twisted coefficients.
In this paper we consider the problem of proving properties of infinite behaviour of formalisms suitable to describe (infinite state) systems with recursion and parallelism. As a formal setting, we consider the framework of Process…
Nearly linear recurrences are a generalisation of linear recurrences and are instances of linear time-invariant systems in control theory and linear constraint loops in program analysis. In this paper we formulate the Positivity Problem for…
A multiparameter class of integrable systems is introduced.
We show how security type systems from the literature of language-based noninterference can be represented more directly as predicates defined by structural recursion on the programs. In this context, we show how our uniform syntactic…
Results concerning recurrence and ergodicity are proved in an abstract Hilbert space setting based on the proof of Khintchine's recurrence theorem for sets, and on the Hilbert space characterization of ergodicity. These results are carried…
We present some results, both rigorously mathematical and computational, showing unexpected relations between different identities expressing nilpotence in nonassociative algebras, and formulate a number of conjectural generalizations and…
Let R be a ring with the set of nilpotents Nil(R). We prove that the following are equivalent: (i) Nil(R) is additively closed, (ii) Nil(R) is multiplicatively closed and R satisfies Koethe's conjecture, (iii) Nil(R) is closed under the…
In this paper, we introduce and study the notion of super-recurrence of operators. We investigate some properties of this class of operators and show that it shares some characteristics with supercyclic and recurrent operators. In…
An $\infty$-step nilsystem is an inverse limit of minimal nilsystems. In this article is shown that a minimal distal system is an $\infty$-step nilsystem if and only if it has no nontrivial pairs with arbitrarily long finite IP-independence…
We study the recurrence of the product of n functions, each of which satisfies the same recurrence relation.
It is well-known that for any non-constant polynomial $P$ with integer coefficients the sequence $(P(n))_{ n\in \mathbb N}$ has the property that there are infinitely many prime numbers dividing at least one term of this sequence.…
Self-similarity is the property of a system being similar to a part of itself. We posit that a special class of behaviourally self-similar systems exhibits a degree of resilience to adversarial behaviour. We formalise the notions of system,…
Let X be a subshift satisfy non-uniform structure. In this paper, we give quantitative estimate of the recurrence sets. These results can be applied to a large class of symbolic systems, including beta-shifts, S-gap shifts and their…