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
T1  - On multisets, interpolated multiple zeta values and limit laws.
JF  - Electronic Journal of Combinatorics
N2  - In this work we discuss a parameter σ on weighted k-element multisets of [n]={1,…,n}. The sums of weighted k-multisets are related to k-subsets, k-multisets, as well as special instances of truncated interpolated multiple zeta values. We study properties of this parameter using symbolic combinatorics. We rederive and extend certain identities for ζtn({m}k). Moreover, we introduce random variables on the k-element multisets and derive their distributions, as well as limit laws for k or n tending to infinity.
KW  - k-multisets
KW  - k-subsets
KW  - truncated-multiple-zeta-values
KW  - interpolated-multiple-zeta-values
KW  - harmonic-numbers
Y1  - 
IS  - Vol. 29, Issue 1
ER  - 
TY  - JOUR
A1  - Hoffmann, Michael E.
A1  - Kuba, Markus
T1  - Logarithmic integrals, zeta values, and tiered binomial coeffcients
JF  - Monatshefte fuer Mathematik
KW  - Integrals
KW  - Binomial
KW  - Coefficient
Y1  - 
ER  - 
TY  - JOUR
A1  - Hoffman, Michael E.
A1  - Kuba, Markus
A1  - Levy, Moti
A1  - Louchard, Guy
T1  - An Asymptotic Series for an Integral
JF  - Ramanujan Journal
KW  - asymtotic
KW  - integral
Y1  - 2020
ER  - 
TY  - JOUR
A1  - Hoffmann, Michael E.
A1  - Kuba, Markus
A1  - Levy, Moti
A1  - Louchard, Guy
T1  - An Asymptotic Series for an Integral
JF  - Ramanujan Journal
KW  - Asymptotic
KW  - Integral
Y1  - 
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  - JOUR
A1  - Kuba, Markus
T1  - A Note on the generating function of p-Bernoulli numbers
JF  - Quaestiones Mathematicae
KW  - Mathematics
Y1  - 
ER  - 
TY  - JOUR
A1  - Kuba, Markus
A1  - Sulzbach, Henning
T1  - On martingale tail sums in affine two-color urn models with multiple drawings
JF  - Journal of Applied Probability
KW  - Probability Calculation
Y1  - 2018
VL  - 54
IS  - 1
SP  - 96
EP  - 117
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  -