TY  - JOUR
A1  - Kuba, Markus
A1  - Panholzer, Alois
T1  - On bucket increasing trees, clustered increasing trees and increasing diamonds
JF  - Combinatorics, Probability and Computing
N2  - In this work we analyse bucket increasing tree families. We introduce two simple stochastic growth processes, generating random bucket increasing trees of size n, complementing the earlier result of Mahmoud and Smythe (1995, Theoret. Comput. Sci.144 221–249.) for bucket recursive trees. On the combinatorial side, we define multilabelled generalisations of the tree families d-ary increasing trees and generalised plane-oriented recursive trees. Additionally, we introduce a clustering process for ordinary increasing trees and relate it to bucket increasing trees. We discuss in detail the bucket size two and present a bijection between such bucket increasing tree families and certain families of graphs called increasing diamonds, providing an explanation for phenomena observed by Bodini et al. (2016, Lect. Notes Comput. Sci.9644 207–219.). Concerning structural properties of bucket increasing trees, we analyse the tree parameter Kn . It counts the initial bucket size of the node containing label n in a tree of size n and is closely related to the distribution of node types. Additionally, we analyse the parameters descendants of label j and degree of the bucket containing label j, providing distributional decompositions, complementing and extending earlier results (Kuba and Panholzer (2010), Theoret. Comput. Sci.411(34–36) 3255–3273.).
KW  - bucket-increasing-trees
KW  - clustered-trees
KW  - stochastic-growth-processes
KW  - descendants
KW  - nodedegrees
Y1  - 2021
IS  - Volume 31 , Issue 4
SP  - 629
EP  - 661
ER  - 
TY  - JOUR
A1  - Kuba, Markus
A1  - Panholzer, Alois
T1  - A Note on Harmonic number identities, Stirling series and multiple zeta values
JF  - International Journal of Number Theory
KW  - Multiple zeta values
KW  - Harmonic numbers
KW  - Arakawa–Kaneko zeta function
KW  - Stirling series
Y1  - 2020
VL  - 15
IS  - 07
SP  - 1323
EP  - 1348
ER  - 
TY  - JOUR
A1  - Kuba, Markus
A1  - Panholzer, Alois
T1  - Stirling permutations containing a single pattern of length three
JF  - The Australasian Journal of Combinatorics
KW  - Stirling permutations
Y1  - 2020
VL  - 74
IS  - 2
SP  - 216
EP  - 239
ER  - 
TY  - CHAP
A1  - Kuba, Markus
A1  - Panholzer, Alois
T1  - Combinatorial analysis of growth models for series-parallel networks.
T2  - Proceedings of the 27th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA) 2016
KW  - Mathematics
KW  - Growth Model
Y1  - 2018
ER  - 
TY  - JOUR
A1  - Kuba, Markus
A1  - Panholzer, Alois
T1  - Combinatorial families of multilabelled increasing trees and hook-length formulas.
JF  - Discrete Mathematics
KW  - Mathematical Trees
KW  - Mathematics
Y1  - 2018
ER  - 
TY  - GEN
A1  - Kuba, Markus
A1  - Panholzer, Alois
T1  - Combinatorial analysis of growth models for series-parallel networks.
KW  - Mathematics
KW  - Combinatorics
Y1  - 2018
ER  - 
TY  - JOUR
A1  - Kuba, Markus
A1  - Panholzer, Alois
T1  - On moment sequences and mixed Poisson distributions.
JF  - Probability Surveys
KW  - Mathematics
KW  - Statistical Distributions
Y1  - 2018
ER  - 
TY  - JOUR
A1  - Kuba, Markus
A1  - Panholzer, Alois
T1  - Tree evolution processes for bucket increasing trees
JF  - Discrete Mathematics
N2  - 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.
KW  - Increasing trees
KW  - multilabelled trees
KW  - tree evolution processes
Y1  - 
U6  - http://dx.doi.org/https://doi.org/10.1016/j.disc.2023.113443
VL  - Vol. 346
IS  - Issue 7
SP  - 113443
ER  -