# Stephan Wagner

Professor at Department of Mathematics; Academic staff

- Telephone:
- +46 18 471 32 88
- E-mail:
- stephan.wagner@math.uu.se
- Visiting address:
- Ångströmlaboratoriet, Lägerhyddsvägen 1
- Postal address:
- Box 480

751 06 UPPSALA

Download contact information for Stephan Wagner at Department of Mathematics; Academic staff

Professor at Department of Mathematics; Probability Theory and Combinatorics

- Telephone:
- +46 18 471 32 88
- E-mail:
- stephan.wagner@math.uu.se
- Visiting address:
- Ångströmlaboratoriet, Lägerhyddsvägen 1
- Postal address:
- Box 480

751 06 UPPSALA

More information is available to staff who log in.

## Short presentation

My research interests are mainly in discrete mathematics, especially combinatorial probability (random trees, random graphs and other random structures), enumerative and analytic combinatorics, and graph theory.

## Biography

2000 - 2006 Studies in mathematics at TU Graz, Austria

2007 - 2019 Department of Mathematical Sciences, Stellenbosch University, South Africa

2020 - current Department of Mathematics, Uppsala University

## Research

Recent publications and preprints:

2020

- On the minimal Hamming weight of a multi-base representation, Journal of Number Theory 208 (2020), 168-179; with D. Krenn and V. Suppakitpaisarn. Preprint: [pdf]
- Inducibility of d-ary trees, Discrete Mathematics 343/2 (2020), 111671 (15 pages); with E. Czabarka, A. A. V. Dossou-Olory and L. Székely. Preprint: [pdf]
- A central limit theorem for almost local additive tree functionals, Algorithmica 82/3 (2020), 642-679; with D. Ralaivaosaona and M. Šileikis. Preprint: [pdf]
- On the distance spectral radius of trees with given degree sequence; Discussiones Mathematicae Graph Theory 40/2 (2020), 495-524; with K. Dadedzi and V. Razanajatovo Misanantenaina.
- On the number of increasing trees with label repetitions, Discrete Mathematics 343/8 (2020), 111722 (12 pages); with O. Bodini, A. Genitrini and B. Gittenberger. Preprint: [pdf]
- The average size of independent sets of graphs, European Journal of Mathematics 6 (2020), 561-576; with E. O. D. Andriantiana and V. Razanajatovo Misanantenaina. Preprint: [pdf]
- The average size of matchings in graphs, Graphs and Combinatorics 36 (2020), 539-560; with E. O. D. Andriantiana and V. Razanajatovo Misanantenaina. Preprint: [pdf]
- Matchings in graphs with a given number of cuts, Discrete Applied Mathematics 283 (2020), 473-481; with J. Liu and F. Huang. Preprint: [pdf]
- Block statistics in subcritical graph classes, Proceedings of the 31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2020); Leibniz International Proceedings in Informatics 159, Article 24; with C. Requilé and D. Ralaivaosaona.
- On the probability that a random digraph is acyclic, Proceedings of the 31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2020); Leibniz International Proceedings in Informatics 159, Article 25; with D. Ralaivaosaona and V. Rasendrahasina.
- On the Collection of Fringe Subtrees in Random Binary Trees, Proceedings of the 14th Latin American Theoretical Informatics Symposium (LATIN 2020), São Paulo, Brazil; Lecture Notes in Computer Science 12118 (2020), 546-558; with L. Seelbach Benkner. Preprint: [pdf]
- The number of distinct adjacent pairs in geometrically distributed words, Discrete Mathematics and Theoretical Computer Science 22/4 (2020), #10 (18 pages); with M. Archibald, A. Blecher, C. Brennan, A. Knopfmacher and M. D. Ward.
- On two subclasses of Motzkin paths and their relation to ternary trees, in Algorithmic Combinatorics - Enumerative Combinatorics, Special Functions and Computer Algebra (V. Pillwein and C. Schneider, eds.), Springer 2020; with H. Prodinger and S. Selkirk. Preprint: [pdf]

2021

- Irrationality of growth constants associated with polynomial recursions, Journal of Integer Sequences 24/1 (2021), article 21.1.6 (9 pages); with V. Ziegler.
- Extremal trees with fixed degree sequence, Electronic Journal of Combinatorics 28/1 (2021), P 1.1 (34 pages); with E. O. D. Andriantiana and V. Razanajatovo Misanantenaina.
- On the maximum mean subtree order of trees, European Journal of Combinatorics 97 (2021), 103388 (19 pages); with S. Cambie and H. Wang. Preprint: [pdf]
- Further results on the inducibility of d-ary trees. Australasian Journal of Combinatorics 81 (2021), 1-24; with A. A. V. Dossou-Olory.
- On the probability that a random subtree is spanning. Journal of Graph Theory 98/2 (2021), 195-215. Preprint: [pdf]

2022

- Trees with minimum number of infima closed sets. Discrete Mathematics 345/5 (2022), 112793 (20 pages); with E. O. D. Andriantiana. Preprint: [pdf]
- Trees in Many Contexts. Notices of the American Mathematical Society 69/2 (2022), 284-286; with H. Smith Blake, M. Bóna, E. Czabarka and H. Wang.
- Steiner Wiener index and line graphs of trees. Discrete Mathematics Letters (special issue dedicated to the memory of Nenad Trinajstić) 9 (2022), 86-91; with M. Kovše and V. Razanajatovo Misanantenaina.
- A polynomial associated with rooted trees and specific posets, Transactions on Combinatorics 11/3 (2022), 255-279; with V. Razanajatovo Misanantenaina.
- Uncovering a random tree.
*33rd International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms,*Art. No. 10, 17 pp., LIPIcs. Leibniz Int. Proc. Inform., 225; with B. Hackl and A. Panholzer. - Automorphisms of random trees.
*33rd International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms,*Art. No. 16, 16 pp., LIPIcs. Leibniz Int. Proc. Inform., 225; with C. Olsson. - Maximum number of subtrees in cacti and block graphs.
*Aequationes Math.*96/5 (2022), 1027-1040; with J. Li, K. Xu, T. Zhang and H. Wang. - Gini index on generalized r-partitions.
*Math. Slovaca*72/5 (2022), 1129-1144; with T. Mansour, M. Schork and M. Shattuck. - Distinct Fringe Subtrees in Random Trees,
*Algorithmica*84 (2022), no. 12, 3686–3728 ; with L. Seelbach Benkner. Preprint: [pdf]

2023

- On the mean subtree order of trees under edge contraction, Journal of Graph Theory 102/3 (2023), 535-551; with Z. Luo, K. Xu and H. Wang.
- Enumeration of Generalized Dyck Paths Based on the Height of Down-Steps Modulo k. Electronic Journal of Combinatorics 30/1 (2023), P1.26 (18 pages); with C. Heuberger and S. J. Selkirk.

- Broadcasting induced colourings of random recursive trees and preferential attachment trees, to appear in Random Structures & Algorithms; with C. Desmarais and C. Holmgren. Preprint: [pdf]
- Refined enumeration of k-plane trees and k-noncrossing trees, to appear in Annals of Combinatorics; with I. O. Okoth. Preprint: [pdf]

Preprints

- Limits of subcritical random graphs and random graphs with excluded minors; with A. Georgakopoulos. Preprint: [pdf]
- The birth of the strong components; with É. de Panafieu, S. Dovgal, D. Ralaivaosaona and V. Rasendrahasina. Preprint: [pdf]
- Convex characters, algorithms and matchings; with S. Kelk and R. Meuwese. Preprint: [pdf]
- Average Case Analysis of Leaf-Centric Binary Tree Sources; with M. Lohrey and L. Seelbach Benkner. Preprint: [pdf]
- On the distribution of eigenvalues of increasing trees; with K. Dadedzi. Preprint: [pdf]
- Trees maximizing the number of almost-perfect matchings; with S. Cambie, B. McCoy, G. Sharma and C. Yap. Preprint: [pdf]
- The minimum number of maximal independent sets in twin-free graphs; with S. Cambie. Preprint: [pdf]
- The distribution of the number of automorphisms of random trees; with C. Olsson. Preprint: [pdf]
- Conditioned Galton-Watson trees: The shape functional, and more on the sum of powers of subtree sizes; with J. A. Fill and S. Janson. Preprint: [pdf]
- The Uncover Process for Random Labeled Trees; with B. Hackl and A. Panholzer. Preprint: [pdf]

Older publications (before 2020) can be found here: Old publications

## Publications

### Recent publications

- Bounding Mean Orders of Sub-
*k*-Trees of*k*-Trees (2024) - On the distribution of eigenvalues of increasing trees (2024)
- The birth of the strong components (2024)
- Refined Enumeration of
*k*-plane Trees and*k*-noncrossing Trees (2024) - Broadcasting-induced colorings of preferential attachment trees (2023)

### All publications

#### Articles

- Bounding Mean Orders of Sub-
*k*-Trees of*k*-Trees (2024) - On the distribution of eigenvalues of increasing trees (2024)
- The birth of the strong components (2024)
- Refined Enumeration of
*k*-plane Trees and*k*-noncrossing Trees (2024) - Broadcasting-induced colorings of preferential attachment trees (2023)
- Enumeration of Generalized Dyck Paths Based on the Height of Down-Steps Modulo
*k*(2023) - On the mean subtree order of trees under edge contraction (2023)
- Trees with minimum number of infima closed sets (2022)
- Steiner Wiener index and line graphs of trees (2022)
- Maximum number of subtrees in cacti and block graphs (2022)
- Gini index on generalized r-partitions (2022)
- A POLYNOMIAL ASSOCIATED WITH ROOTED TREES AND SPECIFIC POSETS (2022)
- Distinct Fringe Subtrees in Random Trees (2022)
- Trees in many contexts (2022)
- Extremal trees with fixed degree sequence (2021)
- The number of distinct adjacent pairs in geometrically distributed words (2021)
- On the maximum mean subtree order of trees (2021)
- On the probability that a random subtree is spanning (2021)
- Irrationality of Growth Constants Associated with Polynomial Recursions (2021)