A numeration system based on a strictly increasing sequence of positive integers u0 = 1, u1, u2, . . . expresses a non-negative integer n as a sum n = ∑i j=0 ajuj . In this case we say the string aiai−1 · · · a1a0 is a representation for n. If gcd(u0, u1, . . .) = g, then every sufficiently large multiple of g has some representation. If the lexicographic ordering on the representations is the ...

We examine the performance of parallel algorithms for rst-order linear recurrence on vector computers, evaluate them quantitatively on a simple model of vector computers, and propose new fast algorithms. We also show a result of performance benchmarking of them on actual vector computers.

This study estimates the impact of London’s successful 2012 summer Olympics bid on property prices. Using a self-constructed dataset of a sample of property transactions, we estimate a semilogarithmic hedonic model for Greater London. Applying a difference-in-differences estimator, we find that properties in the host boroughs are sold between 2.1 and 3.3 percent higher, depending on the definit...

In this paper we give an improvement of the degree of the homogeneous linear recurrence with integer coefficients that exponential sums of symmetric Boolean functions satisfy. This improvement is tight. We also compute the asymptotic behavior of symmetric Boolean functions and provide a formula that allows us to determine if a symmetric boolean function is asymptotically not balanced. In partic...

Fix a prime/?. We say that a set S forms a complete residue system modulop if, for all i such that 0 < i < p 1 , there exists s GS such that s = J (mod /?). We say that a set S forms a reduced residue system modulo p if, for all / such that 1 < i < p -1, there exists s GS such that s = i (mod p). In [9], Shah showed that, ifp is a prime and p = 1,9 (mod 10), then the Fibonacci sequence does not...

Let {an}^_ao be a sequence which satisfies a linear recurrence of order k +1. We are herein concerned with the lacunary subsequences {®mn+b}Z=-ao> where m and b are fixed integers, so called because they consist of the terms from {aJ with lacunae, or gaps, of length m between them. In [5], [2], and [3] it has been shown that, for any m and A, the subsequences {amn+b} also satisfy a linear recur...

for all n ∈ N. In dimension k = 2, there is only the case p = 1 to consider. Favre [F] has given necessary and sufficient conditions for a monomial map in dimension 2 to have a regularization π : X → P satisfying (1.2). Diller and Favre [DF] showed that for every bimeromorphic surface map there is such a regularization. Favre and Jonsson [FJ] have shown that the degree sequence of a polynomial ...

In this paper, we consider a two-dimensional model for finite set partitions which arises in conjunction with a special case of a general non-linear recurrence. We investigate properties of some of the related counting sequences, including recurrences and generating functions. In particular, we obtain, by combinatorial arguments, some formulas relating these sequences to the Stirling numbers of...

A beautiful theorem of Zeckendorf states that every positive integer can be uniquely decomposed as a sum of non-consecutive Fibonacci numbers {Fn}, where F1 = 1, F2 = 2 and Fn+1 = Fn + Fn−1. For general recurrences {Gn} with non-negative coefficients, there is a notion of a legal decomposition which again leads to a unique representation, and the number of summands in the representations of uni...

We exhibit a three parameter infinite family of quadratic recurrence relations inspired by the well known Somos sequences. For one infinite subfamily we prove that the recurrence generates an infinite sequence of integers by showing that the same sequence is generated by a linear recurrence (with suitable initial conditions). We also give conjectured relations among the three parameters so that...