Math @ Duke

Publications [#320535] of Ezra Miller
Papers Published
 with Miller, E; Sturmfels, B, Monomial ideals and planar graphs,
in Applied algebra, algebraic algorithms and errorcorrecting codes (Honolulu, HI, 1999), Lecture Notes in Computer Science, edited by M. Fossorier, H. Imai, S. Lin and A. Poli,
Lecture notes in computer science, vol. 1719
(January, 1999),
pp. 1928, Springer, Berlin, ISBN 3540667237 [MR2002h:13041], [doi]
(last updated on 2017/12/12)
Abstract: © SpringerVerlag Berlin Heidelberg 1999. Gröbner basis theory reduces questions about systems of polynomial equations to the combinatorial study of monomial ideals, or staircases. This article gives an elementary introduction to current research in this area. After reviewing the bivariate case, a new correspondence is established between planar graphs and minimal resolutions of monomial ideals in three variables. A brief guide is given to the literature on complexity issues and monomial ideals in four or more variables.


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