Abstract
A class of diamond-shaped combinatorial structures is studied whose enumerating generating functions satisfy differential equations of the form \(f'' = G(f)\), for some function G. In addition to their own interests and being natural extensions of increasing trees, the study of such DAG-structures was motivated by modelling executions of series-parallel concurrent processes; they may also be used in other digraph contexts having simultaneously a source and a sink, and are closely connected to a few other known combinatorial structures such as trees, cacti and permutations. We explore in this extended abstract the analytic-combinatorial aspect of these structures, as well as the algorithmic issues for efficiently generating random instances.
This research was partially supported by the ANR MetACOnc project ANR-15-CE40-0014.
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Notes
- 1.
We limit our discussion in this paper to the situation when \(f'(0)=1\) for simplicity.
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Bodini, O., Dien, M., Fontaine, X., Genitrini, A., Hwang, HK. (2016). Increasing Diamonds. In: Kranakis, E., Navarro, G., Chávez, E. (eds) LATIN 2016: Theoretical Informatics. LATIN 2016. Lecture Notes in Computer Science(), vol 9644. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-49529-2_16
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DOI: https://doi.org/10.1007/978-3-662-49529-2_16
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