On sequential growth of trees subject to various labeling constraints: from enumeration to probability theory

Document Type : Original Article

Author

• Thierry Huillet

Laboratoire de Physique Théorique et Modélisation. CY Cergy Paris University, France

10.22067/smps.2024.45214

Abstract

Trees, as loop-free graphs, are fundamental hierarchical structures of Nature. Depending on the way their constitutive atoms are labeled, their growth obeys different sequential dynamics when a new atom is being appended to a current tree, possibly forming a new tree. Randomized versions of the underlying counting problems are shown to lead, in general, to Markovian triangular sequences.

Keywords

• Combinatorial probability
• Distinguishability
• Forests
• Markovian‎ ‎triangular sequences
• Randomization
• Simply generated and increasing trees

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