Planar graphs as minimal resolutions of trivariate monomial ideals
Publication
, Journal Article
Miller, E
Published in: Documenta Mathematica
January 1, 2002
We introduce the notion of rigid embedding in a grid surface, a new kind of plane drawing for simple triconnected planar graphs. Rigid embeddings provide methods to (1) find well-structured (cellular, here) minimal free resolutions for arbitrary monomial ideals in three variables: (2) strengthen the Brightwell-Trotter bound on the order dimension of triconnected planar maps by giving a geometric reformulation: and (3) generalize Schnyder's angle coloring of planar triangulations to arbitrary triconnected planar maps via geometry. The notion of rigid embedding is stable under duality for planar maps, and has certain uniqueness properties.
Duke Scholars
Published In
Documenta Mathematica
ISSN
1431-0635
Publication Date
January 1, 2002
Volume
7
Issue
1
Start / End Page
43 / 90
Related Subject Headings
- General Mathematics
- 4904 Pure mathematics
- 0101 Pure Mathematics
Citation
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ICMJE
MLA
NLM
Miller, E. (2002). Planar graphs as minimal resolutions of trivariate monomial ideals. Documenta Mathematica, 7(1), 43–90.
Miller, E. “Planar graphs as minimal resolutions of trivariate monomial ideals.” Documenta Mathematica 7, no. 1 (January 1, 2002): 43–90.
Miller E. Planar graphs as minimal resolutions of trivariate monomial ideals. Documenta Mathematica. 2002 Jan 1;7(1):43–90.
Miller, E. “Planar graphs as minimal resolutions of trivariate monomial ideals.” Documenta Mathematica, vol. 7, no. 1, Jan. 2002, pp. 43–90.
Miller E. Planar graphs as minimal resolutions of trivariate monomial ideals. Documenta Mathematica. 2002 Jan 1;7(1):43–90.
Published In
Documenta Mathematica
ISSN
1431-0635
Publication Date
January 1, 2002
Volume
7
Issue
1
Start / End Page
43 / 90
Related Subject Headings
- General Mathematics
- 4904 Pure mathematics
- 0101 Pure Mathematics