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  "body": "\n## Summary\n\nIn [[combinatorics|0JKW7W7XFR]], a branch of mathematics, a **weighted matroid** is a matroid endowed with a function that assigns a weight to each element. Formally, let $M = (E, I)$ be a matroid, where *E* is the set of elements and *I* is the family of independent set. A weighted matroid has a *weight function* $w : E \\rightarrow \\mathbb{R}^+$ for assigns a strictly positive weight to each element of $E$. We extend the function to subsets of $E$ by summation; $w(A)$ is the sum of $w(x)$ over $x$ in $A$.\n",
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