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  "path": "/abs/2603.10251v1",
  "publishedAt": "2026-03-12T00:00:00.000Z",
  "site": "https://arxiv.org",
  "tags": [
    "Mathilde Bouvel",
    "Valentin Féray",
    "Xavier Goaoc",
    "Florent Koechlin"
  ],
  "textContent": "**Authors:** Mathilde Bouvel, Valentin Féray, Xavier Goaoc, Florent Koechlin\n\nChirotopes are a common combinatorial abstraction of (planar) point sets. In this paper we investigate decomposition methods for chirotopes, and their application to the problem of counting the number of triangulations supported by a given planar point set. In particular, we generalize the convex and concave sums operations defined by Rutschmann and Wettstein for a particular family of chirotopes (which they call chains), and obtain a precise asymptotic estimate for the number of triangulations of the double circle, using a functional equation and the kernel method.",
  "title": "Large chirotopes with computable numbers of triangulations"
}