Geometric vertex decomposability for polynomial ideals is an ideal-theoretic generalization of vertex decomposability for simplicial complexes. Indeed, a homogeneous geometrically vertex decomposable ideal is radical and Cohen-Macaulay, and is in the Gorenstein liaison class of a complete intersection (glicci).
In this paper, we initiate an investigation into when the toric ideal
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Keywords: geometric vertex decomposition, toric ideals of graphs, liaison
Cummings, Mike 1; Da Silva, Sergio 2; Rajchgot, Jenna 1; Van Tuyl, Adam 1

@article{ALCO_2023__6_4_965_0, author = {Cummings, Mike and Da Silva, Sergio and Rajchgot, Jenna and Van Tuyl, Adam}, title = {Geometric vertex decomposition and liaison for toric ideals of graphs}, journal = {Algebraic Combinatorics}, pages = {965--997}, publisher = {The Combinatorics Consortium}, volume = {6}, number = {4}, year = {2023}, doi = {10.5802/alco.295}, language = {en}, url = {https://alco.centre-mersenne.org/articles/10.5802/alco.295/} }
TY - JOUR AU - Cummings, Mike AU - Da Silva, Sergio AU - Rajchgot, Jenna AU - Van Tuyl, Adam TI - Geometric vertex decomposition and liaison for toric ideals of graphs JO - Algebraic Combinatorics PY - 2023 SP - 965 EP - 997 VL - 6 IS - 4 PB - The Combinatorics Consortium UR - https://alco.centre-mersenne.org/articles/10.5802/alco.295/ DO - 10.5802/alco.295 LA - en ID - ALCO_2023__6_4_965_0 ER -
%0 Journal Article %A Cummings, Mike %A Da Silva, Sergio %A Rajchgot, Jenna %A Van Tuyl, Adam %T Geometric vertex decomposition and liaison for toric ideals of graphs %J Algebraic Combinatorics %D 2023 %P 965-997 %V 6 %N 4 %I The Combinatorics Consortium %U https://alco.centre-mersenne.org/articles/10.5802/alco.295/ %R 10.5802/alco.295 %G en %F ALCO_2023__6_4_965_0
Cummings, Mike; Da Silva, Sergio; Rajchgot, Jenna; Van Tuyl, Adam. Geometric vertex decomposition and liaison for toric ideals of graphs. Algebraic Combinatorics, Volume 6 (2023) no. 4, pp. 965-997. doi : 10.5802/alco.295. https://alco.centre-mersenne.org/articles/10.5802/alco.295/
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