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arxiv: 1111.3061 · v1 · submitted 2011-11-13 · 🧮 math.PR · math.CO

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Hultman numbers, polygon gluings and matrix integrals

Nikita Alexeev , Peter Zograf
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classification 🧮 math.PR math.CO
keywords hultmannumbersgenomegluingsintegralspolygonalternatingapproach
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The Hultman numbers enumerate permutations whose cycle graph has a given number of alternating cycles (they are relevant to the Bafna-Pevzner approach to genome comparison and genome rearrangements). We give two new interpretations of the Hultman numbers: in terms of polygon gluings and as integrals over the space of complex matrices, and derive some properties of their generating functions.

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