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

Stochastic Models in Probability and Statistics

دوره 1، شماره 1، مهر 2024، صفحه 75-104   

نوع مقاله: Original Article

نویسنده

Thierry Huillet^*

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

چکیده

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.

کلیدواژه‌ها

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