English

Tree evolution processes for bucket increasing trees

Combinatorics 2022-06-14 v2 Probability

Abstract

We provide a fundamental result for bucket increasing trees, which gives a complete characterization of all families of bucket increasing trees that can be generated by a tree evolution process. We also provide several equivalent properties, complementing and extending earlier results for ordinary increasing trees to bucket trees. Additionally, we state second order results for the number of descendants of label jj, again extending earlier results in the literature.

Keywords

Cite

@article{arxiv.2206.05101,
  title  = {Tree evolution processes for bucket increasing trees},
  author = {Markus Kuba and Alois Panholzer},
  journal= {arXiv preprint arXiv:2206.05101},
  year   = {2022}
}

Comments

Reference updated; 22 pages; draws upon and solves an open problem of arXiv:2003.06450

R2 v1 2026-06-24T11:46:35.368Z