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Betti numbers of
order-preserving graph homomorphisms
Lauren Guerra and Steven Klee
Vol. 5 (2012), No. 1, 67–80
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Abstract |
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For graphs and with totally ordered vertex sets, a function mapping the vertex set of to the vertex set of is an order-preserving homomorphism from to if it is nondecreasing on the vertex set of and maps edges of to edges of . In this paper, we study order-preserving homomorphisms whose target graph is the complete graph on vertices. By studying a family of graphs called nonnesting arc diagrams, we are able to count the number of order-preserving homomorphisms (and more generally the number of order-preserving multihomomorphisms) mapping any fixed graph to the complete graph . |
Keywords
graph homomorphisms, Betti numbers, nonnesting partitions
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Mathematical Subject Classification 2010
Primary: 13D02
Secondary: 05A18, 06A06, 05C30
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Milestones
Received: 27 May 2011
Accepted: 11 July 2011
Published: 28 April 2012
Communicated by Jim Haglund
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Authors |
| Lauren Guerra | |
| Mathematical Sciences Building One Shields Ave. University of California Davis, CA 95616 United States |
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| Steven Klee | |
| Mathematical Sciences Building One Shields Ave. University of California Davis, CA 95616 United States |
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| http://www.math.ucdavis.edu/~klee/ | |
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