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Splitting
techniques and Betti numbers of secant powers
Reza Akhtar, Brittany Burns, Haley Dohrmann, Hannah Hoganson, Ola Sobieska and Zerotti Woods
Vol. 9 (2016), No. 5, 737–750
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Abstract |
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Using ideal-splitting techniques, we prove a recursive formula relating the Betti numbers of the secant powers of the edge ideal of a graph to those of the join of with a finite independent set. We apply this result in conjunction with other splitting techniques to compute these Betti numbers for wheels, complete graphs and complete multipartite graphs, recovering and extending some known results about edge ideals. |
Keywords
Betti number, edge ideal, secant power, complete graph,
complete bipartite graph
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Mathematical Subject Classification 2010
Primary: 13D02
Secondary: 05C25
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Milestones
Received: 31 December 2014
Revised: 23 July 2015
Accepted: 27 October 2015
Published: 25 August 2016
Communicated by Scott T. Chapman
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Authors |
| Reza Akhtar | |
| Department of Mathematics Miami University Oxford, OH 45056 United States |
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| Brittany Burns | |
| Department of Mathematics University of Central Florida Orlando, FL 32816 United States |
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| Haley Dohrmann | |
| Department of Mathematics University of Iowa Iowa City, IA 52242 %-1419 United States |
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| Hannah Hoganson | |
| Department of Mathematics University of Utah Salt Lake City, UT 84112 %-0090 United States |
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| Ola Sobieska | |
| Department of Mathematics Texas A&M University College Station, TX 77843 %-3368 United States |
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| Zerotti Woods | |
| Department of Mathematics University of Georgia Athens, GA 30602 United States |
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