@article{KubaVarvak,
  author    = {Kuba, Markus and Varvak, Anna},
  title     = {On Path diagrams and Stirling permutations},
  series = {S{\´e}minaire Lotharingien de Combinatoire},
  journal   = {S{\´e}minaire Lotharingien de Combinatoire},
  number    = {B82c (2021)},
  pages     = {28},
  abstract  = {A permutation can be locally classified according to the four local types: peaks, valleys, double rises and double falls. The corresponding classification of binary increasing trees uses four different types of nodes. Flajolet demonstrated the continued fraction representation of the generating function of local types, using a classical bijection between permutations, binary increasing trees, and suitably defined path diagrams induced by Motzkin paths. The aim of this article is to extend the notion of local types from permutations to k-Stirling permutations (also known as k-multipermutations). We establish a bijection of these local types to node types of (k+1)-ary increasing trees. We present a branched continued fraction representation of the generating function of these local types through a bijection with path diagrams induced by Łukasiewicz paths, generalizing the results from permutations to arbitrary k-Stirling permutations. We further show that the generating function of ordinary Stirling permutation has at least three branched continued fraction representations, using correspondences between non-standard increasing trees, k-Stirling permutations and path diagrams.},
  subject      = {Kettenbruch},
  language  = {en}
}
@article{KubaPanholzer,
  author    = {Kuba, Markus and Panholzer, Alois},
  title     = {Tree evolution processes for bucket increasing trees},
  series = {Discrete Mathematics},
  volume    = {Vol. 346},
  journal   = {Discrete Mathematics},
  number    = {Issue 7},
  doi       = {https://doi.org/10.1016/j.disc.2023.113443},
  pages     = {113443},
  abstract  = {Bucket increasing trees are multilabelled generalizations of increasing trees, where each non-leaf node carries b labels, with a fixed integer. We provide a fundamental result, giving 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 j, again extending earlier results in the literature.},
  subject      = {Increasing trees},
  language  = {en}
}