Closure properties of knapsack semilinear groups
release_graxo2mwuzhp7ja6latfxqufvi
by
Michael Figelius, Markus Lohrey, Georg Zetzsche
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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