Counting and Discrete Morse Theory
DOI:
https://doi.org/10.32473/ufjur.v21i1.108377Keywords:
undergraduate research, discrete Morse theoryAbstract
We examine enumerating discrete Morse functions on graphs up to equivalence by gradient vector fields and by restrictions on the codomain. We give formulae for the number of discrete Morse functions on specific classes of graphs (line, cycle, and bouquet of circles).
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References
Chari, M. K., & Joswig, M. (2005). Complexes of discrete Morse functions. Discrete Mathematics, 302(1-3), 39-51. doi:10.1016/j.disc.2004.07.027
Forman, R. (1998). Morse Theory for Cell Complexes. Advances in Mathematics, 134(1), 90-145. doi:10.1006/aima.1997.1650
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