@article{KubaPanholzer,
  author    = {Kuba, Markus and Panholzer, Alois},
  title     = {On bucket increasing trees, clustered increasing trees and increasing diamonds},
  series = {Combinatorics, Probability and Computing},
  journal   = {Combinatorics, Probability and Computing},
  number    = {Volume 31 , Issue 4},
  pages     = {629 -- 661},
  abstract  = {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.).},
  subject      = {bucket-increasing-trees},
  language  = {en}
}
@article{Kuba,
  author    = {Kuba, Markus},
  title     = {On multisets, interpolated multiple zeta values and limit laws.},
  series = {Electronic Journal of Combinatorics},
  journal   = {Electronic Journal of Combinatorics},
  number    = {Vol. 29, Issue 1},
  abstract  = {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.},
  subject      = {k-multisets},
  language  = {en}
}
@article{HoffmannKuba,
  author    = {Hoffmann, Michael E. and Kuba, Markus},
  title     = {Logarithmic integrals, zeta values, and tiered binomial coeffcients},
  series = {Monatshefte fuer Mathematik},
  journal   = {Monatshefte fuer Mathematik},
  subject      = {Integrals},
  language  = {en}
}
@article{HoffmanKubaLevyetal.,
  author    = {Hoffman, Michael E. and Kuba, Markus and Levy, Moti and Louchard, Guy},
  title     = {An Asymptotic Series for an Integral},
  series = {Ramanujan Journal},
  journal   = {Ramanujan Journal},
  subject      = {asymtotic},
  language  = {en}
}
@article{HoffmannKubaLevyetal.,
  author    = {Hoffmann, Michael E. and Kuba, Markus and Levy, Moti and Louchard, Guy},
  title     = {An Asymptotic Series for an Integral},
  series = {Ramanujan Journal},
  journal   = {Ramanujan Journal},
  subject      = {Asymptotic},
  language  = {en}
}
@article{KubaPanholzer,
  author    = {Kuba, Markus and Panholzer, Alois},
  title     = {A Note on Harmonic number identities, Stirling series and multiple zeta values},
  series = {International Journal of Number Theory},
  volume    = {15},
  journal   = {International Journal of Number Theory},
  number    = {07},
  pages     = {1323 -- 1348},
  subject      = {Multiple zeta values},
  language  = {en}
}
@article{KubaPanholzer,
  author    = {Kuba, Markus and Panholzer, Alois},
  title     = {Stirling permutations containing a single pattern of length three},
  series = {The Australasian Journal of Combinatorics},
  volume    = {74},
  journal   = {The Australasian Journal of Combinatorics},
  number    = {2},
  pages     = {216 -- 239},
  subject      = {Stirling permutations},
  language  = {en}
}
@article{Kuba,
  author    = {Kuba, Markus},
  title     = {A Note on the generating function of p-Bernoulli numbers},
  series = {Quaestiones Mathematicae},
  journal   = {Quaestiones Mathematicae},
  subject      = {Mathematics},
  language  = {en}
}
@article{KubaSulzbach,
  author    = {Kuba, Markus and Sulzbach, Henning},
  title     = {On martingale tail sums in affine two-color urn models with multiple drawings},
  series = {Journal of Applied Probability},
  volume    = {54},
  journal   = {Journal of Applied Probability},
  number    = {1},
  pages     = {96 -- 117},
  subject      = {Probability Calculation},
  language  = {en}
}
@inproceedings{KubaPanholzer,
  author    = {Kuba, Markus and Panholzer, Alois},
  title     = {Combinatorial analysis of growth models for series-parallel networks.},
  series = {Proceedings of the 27th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA) 2016},
  booktitle = {Proceedings of the 27th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA) 2016},
  subject      = {Mathematics},
  language  = {en}
}
@article{KubaPanholzer,
  author    = {Kuba, Markus and Panholzer, Alois},
  title     = {Combinatorial families of multilabelled increasing trees and hook-length formulas.},
  series = {Discrete Mathematics},
  journal   = {Discrete Mathematics},
  subject      = {Mathematical Trees},
  language  = {de}
}
@misc{KubaPanholzer,
  author    = {Kuba, Markus and Panholzer, Alois},
  title     = {Combinatorial analysis of growth models for series-parallel networks.},
  subject      = {Mathematics},
  language  = {en}
}
@article{KubaPanholzer,
  author    = {Kuba, Markus and Panholzer, Alois},
  title     = {On moment sequences and mixed Poisson distributions.},
  series = {Probability Surveys},
  journal   = {Probability Surveys},
  subject      = {Mathematics},
  language  = {en}
}
@misc{Kuba,
  author    = {Kuba, Markus},
  title     = {Limit laws for urn models with multiple drawings},
  subject      = {Urn Models},
  language  = {en}
}
@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{OlaverriMonrealErreaMorenoDiazAlvarezetal.,
  author    = {Olaverri-Monreal, Cristina and Errea-Moreno, Javier and Diaz-Alvarez, Alberto and Biurrun-Quel, Carlos and Serrano-Arriezu, Luis and Kuba, Markus},
  title     = {Connection of the SUMO Microscopic Traffic Simulator and the Unity 3D Graphic Engine to Evaluate V2X Communication-Based Systems},
  series = {Sensors},
  journal   = {Sensors},
  subject      = {Traffic},
  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}
}