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  "path": "/2026/02/25/cosmin-pohoata-the-cayley-bacharach-theorem-and-its-applications/",
  "publishedAt": "2026-02-25T19:35:11.000Z",
  "site": "https://gilkalai.wordpress.com",
  "tags": [
    "The Cayley-Bacharach theorem and its applications",
    "his earlier post",
    "another post",
    "original paper"
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  "textContent": "> The Cayley-Bacharach theorem and its applications\n\nCosmin Pohoata’s new and beautiful blog post presents several combinatorial applications of the Cayley–Bacharach theorem. Let me also mention his earlier post, in which he gave a new proof of Jamison’s direction tree theorem: every finite noncollinear point set in  admits a admits a direction tree—that is, a spanning tree whose edges have pairwise distinct directions.\n\nIn January, after a long break, Cosmin wrote another post presenting an entropy-based proof of an interesting product–sum theorem over finite fields.\n\nSome direction trees from Jamison’s original paper\n\nBy Gil Kalai",
  "title": "Cosmin Pohoata: The Cayley-Bacharach theorem and its applications"
}