Hurwitz numbers for real polynomials
| Autor: | Dimitri Zvonkine, Ilia Itenberg |
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| Rok vydání: | 2018 |
| Předmět: |
Pure mathematics
Polynomial Logarithm Degree (graph theory) General Mathematics media_common.quotation_subject 010102 general mathematics Order (ring theory) 0102 computer and information sciences Infinity 01 natural sciences Mathematics - Algebraic Geometry 010201 computation theory & mathematics ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION FOS: Mathematics Mathematics - Combinatorics Combinatorics (math.CO) 0101 mathematics Real line Algebraic Geometry (math.AG) Branch point media_common Mathematics Sign (mathematics) |
| DOI: | 10.5169/seals-787373 |
| Popis: | We consider the problem of defining and computing real analogs of polynomial Hurwitz numbers, in other words, the problem of counting properly normalized real polynomials with fixed ramification profiles over real branch points. We show that, provided the polynomials are counted with an appropriate sign, their number does not depend on the order of the branch points on the real line. We study generating series for the invariants thus obtained, determine necessary and sufficient conditions for the vanishing and nonvanishing of these generating series, and obtain a logarithmic asymptotic for the invariants as the degree of the polynomials tends to infinity. 40 pages |
| Databáze: | OpenAIRE |
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