Closure properties of knapsack semilinear groups release_graxo2mwuzhp7ja6latfxqufvi

by Michael Figelius, Markus Lohrey, Georg Zetzsche

Released as a article .

2019  

Abstract

We show that the following group constructions preserve the semilinearity of the solution sets for knapsack equations (equations of the form g_1^x_1... g_k^x_k = g in a group G, where the variables x_1, ..., x_k take values in the natural numbers): graph products, amalgamated free products with finite amalgamated subgroups, HNN-extensions with finite associated subgroups, and finite extensions. Moreover, we study the dependence of the so-called magnitude for the solution set of a knapsack equation (the magnitude is a complexity measure for semi-linear sets) with respect to the length of the knapsack equation (measured in number of generators). We investigate, how this dependence changes under the above group operations.
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Date   2019-11-28
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arXiv  1911.12857v1
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