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| ==== abstract ==== | ==== abstract ==== | ||
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| The zig-zag is a graph product enabling the recursive construction | The zig-zag is a graph product enabling the recursive construction | ||
| + | of explicit expander families. These graphs are remarkable in that | ||
| + | the proof of expansion relies on combinatorial rather than | ||
| + | algebraic arguments, and is considerably simpler than that of | ||
| + | other known constructions. | ||
| + | |||
| + | We will first present the zig-zag product, its expansion | ||
| + | properties and the constructions it yields. We will then | ||
| + | explore the link with the semi-direct product of | ||
| + | groups, which was used to show that expansion of Cayley | ||
| + | graphs is not a group property (i.e. it depends on the | ||
| + | choice of generators). | ||