Q-permutations are very easy mathematical structures (essentially consisting in a permutation with attached a natural number) able to encode the basic information concerning any compact and connected orientable surface. At the first place, we introduce the notion of pq-permutation: an enrichment of q-permutations able to characterize surfaces in general: not only orientable but also non-orientable. In the second place, we provide a rewriting system on sets of pq-permutations which is able to compute, in a very easy and intuitive way, the quotient surface corresponding to any given polygonal presentation. The system at issue is shown to enjoy both the properties of strong normalization and strict strong confluence. Finally, we recover the classification theorem by using the specific combinatorial tools here provided.
Computing surfaces via pq-permutations
PULCINI, GABRIELE
2008-01-01
Abstract
Q-permutations are very easy mathematical structures (essentially consisting in a permutation with attached a natural number) able to encode the basic information concerning any compact and connected orientable surface. At the first place, we introduce the notion of pq-permutation: an enrichment of q-permutations able to characterize surfaces in general: not only orientable but also non-orientable. In the second place, we provide a rewriting system on sets of pq-permutations which is able to compute, in a very easy and intuitive way, the quotient surface corresponding to any given polygonal presentation. The system at issue is shown to enjoy both the properties of strong normalization and strict strong confluence. Finally, we recover the classification theorem by using the specific combinatorial tools here provided.
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