Related papers: Recurrence relations versus succession rules

We show that, if an integer sequence is given by a linear recurrence of constant rational coefficients, then it can be represented as the difference of two arithmetic terms with exponentiation, which do not contain any irrational constant.…

Within the context of the binomial model, we analyse sequences of values that are almost-uniform and we discuss a prediction method called the frequent outcome approach, in which the outcome that has occurred the most in the observed trials…

We define a sequence of positive integers recursively, where each term is determined as follows: starting with a given positive integer, if the term is odd, the next is the sum of its positive divisors; if the term is even, the subsequent…

We consider a group of voters that needs to decide between two candidates. We propose a novel family of neutral and strategy-proof rules, which we call sequential unanimity rules. By demonstrating their formal equivalence to the M-winning…

Constant-recursive sequences are those which satisfy a linear recurrence, so that later terms can be obtained as a linear combination of the previous ones. The rank of a constant-recursive sequence is the minimal number of previous terms…

In this article I propose an approach for defining replicability for prediction rules. Motivated by a recent NAS report, I start from the perspective that replicability is obtaining consistent results across studies suitable to address the…

While many production-ready and robust algorithms are available for the task of recommendation systems, many of these systems do not take the order of user's consumption into account. The order of consumption can be very useful and matters…

Many classification problems require decisions among a large number of competing classes. These tasks, however, are not handled well by general purpose learning methods and are usually addressed in an ad-hoc fashion. We suggest a general…

We present a certain generalization of a recent result of M. I. Cirnu on linear recurrence relations with coefficient in progressions [2]. We provide some interesting examples related to some well-known integer sequences, such as Fibonacci…

We derive the necessary and sufficient condition, for a given Polynomial Recurrence Sequence to converge to a given target rational K. By converge, we mean that the Nth term of the sequence, is equal to K, as N tends to positive infinity.…

In [arXiv:1006.4939] the enumeration order reducibility is defined on natural numbers. For a c.e. set A, [A] denoted the class of all subsets of natural numbers which are co-order with A. In definition 5 we redefine co-ordering for rational…

This paper shows that sequential statistical analysis techniques can be generalised to the problem of selecting between alternative forecasting methods using scoring rules. A return to basic principles is necessary in order to show that…

Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…

Labeled infinite trees provide combinatorial interpretations for many integer sequences generated by nested recurrence relations. Typically, such sequences are monotone increasing. Several of these sequences also have straightforward…

Existential rules have been proposed for representing ontological knowledge, specifically in the context of Ontology-Based Query Answering. Entailment with existential rules is undecidable. We focus in this paper on conditions that ensure…

Sequential recommender systems are an important and demanded area of research. Such systems aim to use the order of interactions in a user's history to predict future interactions. The premise is that the order of interactions and…

A simple mechanism for allocating indivisible resources is sequential allocation in which agents take turns to pick items. We focus on possible and necessary allocation problems, checking whether allocations of a given form occur in some or…

This work proposes a novel adaptation of a pretrained sequence-to-sequence model to the task of document ranking. Our approach is fundamentally different from a commonly-adopted classification-based formulation of ranking, based on…

We initiate a general approach for the fast enumeration of permutations with a prescribed number of occurrences of `forbidden' patterns, that seems to indicate that the enumerating sequence is always P-recursive. We illustrate the method…

Representing a word by its co-occurrences with other words in context is an effective way to capture the meaning of the word. However, the theory behind remains a challenge. In this work, taking the example of a word classification task, we…