Trees, parking functions, syzygies, and deformations of monomial ideals

  title={Trees, parking functions, syzygies, and deformations of monomial ideals},
  author={Alexander Postnikov and Boris Z. Shapiro},
  journal={Transactions of the American Mathematical Society},
For a graph G, we construct two algebras whose dimensions are both equal to the number of spanning trees of G. One of these algebras is the quotient of the polynomial ring modulo certain monomial ideal, while the other is the quotient of the polynomial ring modulo certain powers of linear forms. We describe the set of monomials that forms a linear basis in each of these two algebras. The basis elements correspond to G-parking functions that naturally came up in the abelian sandpile model. These… Expand
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