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2016 Depths and Stanley depths of path ideals of spines
Daniel Campos, Ryan Gunderson, Susan Morey, Chelsey Paulsen, Thomas Polstra
Involve 9(1): 155-170 (2016). DOI: 10.2140/involve.2016.9.155


For a special class of trees, namely trees that are themselves a path, a precise formula is given for the depth of an ideal generated by all (undirected) paths of a fixed length. The dimension of these ideals is also computed, which is used to classify which such ideals are Cohen–Macaulay. The techniques of the proofs are shown to extend to provide a lower bound on the Stanley depth of these ideals. Combining these results gives a new class of ideals for which the Stanley conjecture holds.


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Daniel Campos. Ryan Gunderson. Susan Morey. Chelsey Paulsen. Thomas Polstra. "Depths and Stanley depths of path ideals of spines." Involve 9 (1) 155 - 170, 2016.


Received: 2 October 2014; Revised: 22 December 2014; Accepted: 9 January 2015; Published: 2016
First available in Project Euclid: 22 November 2017

zbMATH: 1328.05078
MathSciNet: MR3438451
Digital Object Identifier: 10.2140/involve.2016.9.155

Primary: 05E40 , 13C14 , 13F55
Secondary: 05C05 , 05C25 , 05C65 , 13A15

Keywords: Cohen–Macaulay , depth , Edge ideal , monomial ideal , path ideal

Rights: Copyright © 2016 Mathematical Sciences Publishers


Vol.9 • No. 1 • 2016
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