MODELLING THE STAMP PROBLEM IN TWODIMENSIONAL FORMULATION

A Note on the Postage Stamp Problem

Let h, k be fixed positive integers, and let A be any set of positive integers. Let hA := {a1 + a2 + · · · + ar : ai ∈ A, r ≤ h} denote the set of all integers representable as a sum of no more than h elements of A, and let n(h, A) denote the largest integer n such that {1, 2, . . . , n} ⊆ hA. Let n(h, k) = maxA n(h, A), where the maximum is taken over all sets A with k elements. The purpose of...

Generalizations of the Postage Stamp Problem

The postage stamp problem and its variations are classical problems in elementary number theory. This problem involves finding the largest value that cannot be expressed as a nonnegative linear combination of two relatively prime integers m and p. It turns out that this value can be defined as a function of m and p. An original proof of this fact is the first major goal of this paper. Moreover,...

Structural Time Series Modelling with Stamp 6.02

The structural time series approach involves decomposing a series into components which have a direct interpretation. Usually, three components are considered: a trend, a seasonal component and an irregular component. However, other dynamic processes can also be included in this decomposition. The estimation of the components of this additive decomposition is called signal extraction. A structu...

The Postage Stamp Problem and Essential Subsets in Integer Bases

Plagne recently determined the asymptotic behavior of the function E(h), which counts the maximum possible number of essential elements in an additive basis for N of order h. Here we extend his investigations by studying asymptotic behavior of the function E(h, k), which counts the maximum possible number of essential subsets of size k, in a basis of order h. For a fixed k and with h going to i...

Modelling and Simulation of Embedded Computer Control Systems: Problem Formulation