arXiv Open Access 2019

Eulerian orientations and the six-vertex model on planar map

Mireille Bousquet-Mélou Andrew Elvey Price Paul Zinn-Justin

Lihat Sumber

Abstrak

We address the enumeration of planar 4-valent maps equipped with an Eulerian orientation by two different methods, and compare the solutions we thus obtain. With the first method we enumerate these orientations as well as a restricted class which we show to be in bijection with general Eulerian orientations. The second method, based on the work of Kostov, allows us to enumerate these 4-valent orientations with a weight on some vertices, corresponding to the six vertex model. We prove that this result generalises both results obtained using the first method, although the equivalence is not immediately clear.

Topik & Kata Kunci

math.CO

Penulis (3)

Mireille Bousquet-Mélou

Andrew Elvey Price

Paul Zinn-Justin

Format Sitasi

APA MLA BibTeX

Bousquet-Mélou, M., Price, A.E., Zinn-Justin, P. (2019). Eulerian orientations and the six-vertex model on planar map. https://arxiv.org/abs/1902.07369

Akses Cepat

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Informasi Jurnal

Tahun Terbit: 2019
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓