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The Postage Stamp Problem and Essential Subsets in Integer Bases
Peter Hegarty
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…
Essentialities in additive bases
Peter Hegarty
Let A be an asymptotic basis for N_0 of some order. By an essentiality of A one means a subset P such that A¶is no longer an asymptotic basis of any order and such that P is minima…
The inverse problem for representation functions for general linear forms
Peter Hegarty
The inverse problem for representation functions takes as input a triple (X,f,L), where X is a countable semigroup, f : X --> N_0 \cup {\infty} a function, L : a_1 x_1 + ... + a_h…
Extremal subsets of {1,...,n} avoiding solutions to linear equations in three variables
Peter Hegarty
We refine previous results to provide examples, and in some cases precise classifications, of extremal subsets of {1,...,n} containing no solutions to a wide class of non-invariant…