Rank-3 scale theorems: Difference between revisions
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==== Definition: AG ==== | ==== Definition: AG ==== | ||
''S'' satisfies the ''alternating generator property'' (AG) if it satisfies the following equivalent properties: | ''S'' satisfies the ''alternating generator property'' (AG) if it satisfies the following equivalent properties: | ||
# ''S'' can be built by stacking alternating generators, resulting in a circle of the form either g1 g2 ... g1 g2 g1 g3 or g1 g2 ... g1 g2 g3. | # ''S'' can be built by stacking a single chain of alternating generators, resulting in a circle of the form either g1 g2 ... g1 g2 g1 g3 or g1 g2 ... g1 g2 g3. | ||
# ''S'' is generated by two chains of generators separated by a fixed interval; either both chains are of size ''m'', or one chain has size ''m'' and the second has size ''m-1''. | # ''S'' is generated by two chains of generators separated by a fixed interval; either both chains are of size ''m'', or one chain has size ''m'' and the second has size ''m-1''. | ||