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  "body": "\n## Summary\n\nThe Tutte polynomial $T(x, y)$ is a polynomial in two variables attached to a graph or, more generally, to a [[matroid|PX31ZNYS3Z]].\nIt is the most general invariant that satisfies the deletion–contraction recurrence, and many counting invariants are specializations of it.\nAmong them are the number of [[spanning trees|0S4ZEZM7KE]], the [[chromatic polynomial|0B621RBVS9]], the flow polynomial and the reliability polynomial.\nThe partition function of the Potts model in statistical physics is another specialization.\n\n## Explanations\n\n### L1 human\n\nMany questions about a graph can be answered by removing one edge or squeezing one edge to a point and combining the answers for the two smaller graphs.\nThe Tutte polynomial records all such answers at once.\nPlugging in particular numbers gives particular counts: for example, $T(1, 1)$ is the number of spanning trees of a connected graph.\nFor a triangle, $T(x, y) = x^2 + x + y$, and $T(1, 1) = 3$ is its number of spanning trees.\n",
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