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 - 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 - GEN A1 - Kuba, Markus T1 - Limit laws for urn models with multiple drawings KW - Urn Models Y1 - ER - TY - JOUR A1 - Kuba, Markus A1 - Varvak, Anna T1 - On Path diagrams and Stirling permutations JF - Séminaire Lotharingien de Combinatoire N2 - 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. KW - Kettenbruch KW - Formale Potenzreihe KW - Continued fractions KW - Łukasiewicz paths KW - Path diagrams KW - Stirling permutations KW - Multipermutations KW - Increasing trees Y1 - 2021 IS - B82c (2021) ER - TY - JOUR A1 - Olaverri-Monreal, Cristina A1 - Errea-Moreno, Javier A1 - Diaz-Alvarez, Alberto A1 - Biurrun-Quel, Carlos A1 - Serrano-Arriezu, Luis A1 - Kuba, Markus T1 - Connection of the SUMO Microscopic Traffic Simulator and the Unity 3D Graphic Engine to Evaluate V2X Communication-Based Systems JF - Sensors KW - Traffic KW - Simulator Y1 - 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 -