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Depths and
Stanley depths of path ideals of spines
Daniel Campos, Ryan Gunderson, Susan Morey, Chelsey Paulsen and Thomas Polstra
Vol. 9 (2016), No. 1, 155–170
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Abstract |
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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. |
Keywords
Edge ideal, depth, path ideal, Cohen–Macaulay, monomial
ideal
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Mathematical Subject Classification 2010
Primary: 05E40, 13C14, 13F55
Secondary: 13A15, 05C25, 05C65, 05C05
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Milestones
Received: 2 October 2014
Revised: 22 December 2014
Accepted: 9 January 2015
Published: 17 December 2015
Communicated by Scott T. Chapman
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Authors |
| Daniel Campos | |
| 525 West Mulberry Avenue San Antonio, TX 78212 United States |
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| Ryan Gunderson | |
| Department of Mathematics Duke University Durham, NC 27708 United States |
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| Susan Morey | |
| Department of Mathematics Texas State University 601 University Drive San Marcos, TX 78666 United States |
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| Chelsey Paulsen | |
| East Chapel Hill High School 500 Weaver Dairy Road Chapel Hill, NC 27514 United States |
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| Thomas Polstra | |
| Department of Mathematics University of Missouri 202 Mathematical Sciences Building Columbia, MO 65211 United States |
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