Titlebook: Counting Surfaces; CRM Aisenstadt Chair Bertrand Eynard Book 2016 Springer International Publishing Switzerland 2016 Algebraic geometry.Com

長(zhǎng)矛

Springer International Publishing Switzerland 2016

Amorous

Werner Rittberger,Bernward JenschkeIn this chapter we introduce definitions of maps, which are discrete surfaces obtained by gluing polygons along their sides, and we define generating functions to count them. We also derive Tutte’s equations, which are recursive equations satisfied by the generating functions.

眉毛

In this chapter we introduce the notion of a formal matrix integral, which is very useful for combinatorics, as it turns out to be identical to the generating function of maps of Chap.?.

Ornament

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resilience

https://doi.org/10.1007/978-3-476-03355-0We have seen, in almost all previous chapters, that symplectic invariants and topological recursion play an important role. They give the solution to Tutte’s recursion equation for maps, they give the formal expansion of various matrix integrals, including Kontsevich integral, and they also give the asymptotics of large maps.

哥哥噴涌而出

去才蔑視

Formal Matrix Integrals,In this chapter we introduce the notion of a formal matrix integral, which is very useful for combinatorics, as it turns out to be identical to the generating function of maps of Chap.?.

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天賦

Counting Riemann Surfaces,In the previous chapter, we have computed the asymptotic generating functions of large maps, and we have seen that they are related to the (?.,?.) minimal model.