Scientific papers


  1. Extremal Problems for Topological Indices in Combinatorial Chemistry, Journal of Computational Biology 12/7 (2005), 1004-1013; with R.F. Tichy.
  2. A class of trees and its Wiener index, Acta Applicandae Mathematicae 91/2 (2006), 119-132. Preprint: [pdf]
  3. On the number of decomposable trees, Proceedings of the Fourth Colloquium on Mathematics and Computer Science, Nancy, September 18-22, 2006, pp. 301-308.
  4. The number of spanning trees of finite Sierpinski graphs, Proceedings of the Fourth Colloquium on Mathematics and Computer Science, Nancy, September 18-22, 2006, pp. 411-414; with E. Teufl.
  5. On an identity for the cycle indices of rooted tree automorphism groups, Electronic Journal of Combinatorics 13(1) (2006), N14 (7 pages).
  6. The Fibonacci Number of generalized Petersen graphs, The Fibonacci Quarterly 44/4 (2006), 362-367. Preprint: [pdf]
  7. Extremal trees with respect to Hosoya Index and Merrifield-Simmons Index, MATCH Communications in Mathematical and in Computer Chemistry 57 (2007), 221-233.
  8. Correlation of graph-theoretical indices, SIAM Journal on Discrete Mathematics 21/1 (2007), 33-46. Preprint: [pdf]; see also proof details
  9. On the average Wiener index of degree-restricted trees, Australasian Journal of Combinatorics 37 (2007), 187-203. Preprint: [pdf]
  10. On the number of matchings of a tree, European Journal of Combinatorics 28/4 (2007), 1322-1330. Preprint: [pdf]
  11. Numbers with fixed sum of digits in linear recurrent number systems, The Ramanujan Journal 14/1 (2007), 43-68. Preprint: [pdf]
  12. Graphs, Partitions and Fibonacci Numbers, Discrete Applied Mathematics 155/10 (2007), 1175-1187; with A. Knopfmacher, R.F. Tichy. and V. Ziegler. Preprint: [pdf]
  13. Enumeration problems for classes of self-similar graphs, Journal of Combinatorial Theory, Series A 114/7 (2007), 1254-1277; with E. Teufl. Preprint: [pdf]
  14. Perfect matchings and k-decomposability of increasing trees, Séminaire Lotharingien de Combinatoire B57a (2007), 14 pages; with M. Kuba.
  15. The Fibonacci Number of Fibonacci trees and a related family of polynomial recurrence systems, The Fibonacci Quarterly 45/3 (2007), 247-253. Preprint: [pdf]
  16. Minimal and maximal plateau lengths in Motzkin paths, Proceedings of the 2007 Conference on Analysis of Algorithms, Juan les pins, June 17-22, 2007, pp. 353-362; with H. Prodinger.
  17. Algorithmic generation of molecular graphs with large Merrifield-Simmons index, MATCH Communications in Mathematical and in Computer Chemistry 59/1 (2008), 239-252; with R.F. Tichy. See also programs
  18. Maximizing the number of independent subsets over trees with bounded degree, Journal of Graph Theory 58/1 (2008), 49-68; with C. Heuberger. Preprint available as report 2007-3: [pdf]
  19. The distribution of ascents of size d or more in partitions of n, Combinatorics, Probability and Computing 17/4 (2008), 495-509; with C. Brennan and A. Knopfmacher. Preprint: [pdf]
  20. Combinatorial properties of a general domination problem with parity constraints, Discrete Mathematics 308/24 (2008), 6355-6367; with J. Hatzl. Preprint: [pdf]
  21. Positional number systems with digits forming an arithmetic progression, Monatshefte für Mathematik 155/3-4 (2008), 349-375; with C. Heuberger and H. Prodinger. Preprint available as report 2007-10: [pdf]
  22. Subset counting in trees, Ars Combinatoria 89 (2008), 127-139. Preprint: [pdf]
  23. Joint distributions for movements of elements in Sattolo's and the Fisher-Yates algorithm, Quaestiones Mathematicae 31/4 (2008), 307-344; with G. Louchard and H. Prodinger. Preprint: [pdf]
  24. Asymptotic enumeration on self-similar graphs with two boundary vertices, Discrete Mathematics and Theoretical Computer Science 11/1 (2009), 11-32; with E. Teufl. Preprint: [pdf]
  25. Molecular graphs and the inverse Wiener index problem, Discrete Applied Mathematics 157/7 (2009), 1544-1554; with H. Wang and G. Yu. Preprint: [pdf]; see also Mathematica files
  26. On the parity of the Wiener index, European Journal of Combinatorics 30/4 (2009), 996-1004; with H. Wang. Preprint: [pdf]
  27. On tries, contention trees and their analysis, Annals of Combinatorics 12/4 (2009), 493-507. Preprint: [pdf]
  28. On a Class of Extremal Trees for Various Indices, MATCH Communications in Mathematical and in Computer Chemistry 62/3 (2009), 437-464; with C. Heuberger.
  29. Chemical Trees Minimizing Energy and Hosoya Index, Journal of Mathematical Chemistry 46/1 (2009), 214-230; with C. Heuberger. Preprint available as report 2008-6: [pdf]
  30. Some new results on distance-based graph invariants, European Journal of Combinatorics 30/5 (2009), 1149-1163; with M. H. Khalifeh, H. Yousefi-Azari and A. R. Ashrafi.
  31. The digit generating function of a polynomial, Journal of Number Theory 129/6 (2009), 1325-1337; with H. Prodinger. Preprint: [pdf]
  32. Waring's problem with restrictions on q-additive functions, Mathematica Slovaca 59/3 (2009), 339-348. Preprint: [pdf]
  33. An asymptotic independence theorem for the number of matchings in graphs, Graphs and Combinatorics 25/2 (2009), 239-251; with E. Teufl. Preprint: [pdf]
  34. Almost all trees have an even number of independent sets, Electronic Journal of Combinatorics 16(1) (2009), R93 (10 pages).
  35. On a problem of Ahlswede and Katona, Studia Scientiarum Mathematicarum Hungarica 46/3 (2009), 423-435; with H. Wang. Preprint: [pdf]
  36. The inverse problem for certain tree parameters, Discrete Applied Mathematics 157/15 (2009), 3314 - 3319; with L. Székely and E. Czabarka. Preprint: [pdf]; see also Mathematica file
  37. Spanning forests, electrical networks, and a determinant identity, Proceedings of the 21st International Conference on Formal Power Series and Algebraic Combinatorics, Hagenberg, July 20-24, 2009, pp. 847--858; with E. Teufl.
  38. On the distribution of the longest run in number partitions, The Ramanujan Journal 20/2 (2009), 189-206. Preprint: [pdf]
  39. Exact and asymptotic enumeration of perfect matchings in self-similar graphs, Discrete Mathematics 309/23-24 (2009), 6612-6625; with E. Teufl. Preprint: [pdf]
  40. Determinant identities for Laplace matrices, Linear Algebra and its Applications 432/1 (2010), 441-457; with E. Teufl. Preprint: [pdf]
  41. Deterministic edge-weights in increasing tree families, Combinatorics, Probability and Computing 19/1 (2010), 99-119; with M. Kuba. Preprint: [pdf]
  42. Bijections for a class of labeled plane trees, European Journal of Combinatorics 31/3 (2010), 720-732; with N.S.S. Gu and H. Prodinger. Preprint: [pdf]
  43. Enumeration of matchings in families of self-similar graphs, Discrete Applied Mathematics 158/14 (2010), 1524-1535; with E. Teufl. Preprint: [pdf]
  44. A central limit theorem for integer partitions, Monatshefte für Mathematik 161/1 (2010), 85-114; with M. Madritsch. Preprint: [pdf]
  45. A note on the inverse problem for the Wiener index, MATCH Communications in Mathematical and in Computer Chemistry 64/3 (2010), 639-646.
  46. Records in set partitions, Electronic Journal of Combinatorics 17(1) (2010), R109 (14 pages); with A. Knopfmacher and T. Mansour.
  47. Asymptotics of the extremal values of certain graph parameters in trees with bounded degree, Publicationes Mathematicae Debrecen 77/3-4 (2010), 347-367; with C. Heuberger. Preprint available as report 2007-12: [pdf]
  48. Enumerating set partitions by the number of positions between adjacent occurrences of a letter, Applicable Analysis and Discrete Mathematics 4 (2010), 284-308; with T. Mansour and M. Shattuck.
  49. On unary nodes in tries, Proceedings of the 21st International Meeting on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms, Vienna, June 28 - July 2, 2010, pp. 577--590.
  50. On the number of spanning trees on various lattices, Journal of Physics A 43 (2010), 415001 (8 pages); with E. Teufl. Preprint: [pdf]
  51. On the distribution of depths in increasing trees, Electronic Journal of Combinatorics 17(1), R137 (9 pages) (2010); with M. Kuba.
  52. Maxima and minima of the Hosoya index and the Merrifield-Simmons index: A survey of results and techniques, Acta Applicandae Mathematicae 112/3 (2010), 323-346; with I. Gutman. Preprint: [pdf]
  53. Counting all parity realizable trees, Journal of Combinatorial Mathematics and Combinatorial Computing 75 (2010), 11-32. Preprint: [pdf]
  54. Fibonacci Integers, Journal of Number Theory 131/3 (2011), 440-457; with F. Luca and C. Pomerance. Preprint: [pdf]
  55. On the number of independent subsets in trees with restricted degrees, Mathematical and Computer Modelling 53/5-6 (2011), 678-683; with E. O. D. Andriantiana.
  56. Resistance scaling and the number of spanning trees in self-similar lattices, Journal of Statistical Physics 142/4 (2011), 879-897; with E. Teufl. Preprint: [pdf]
  57. Limit distributions of smallest gap and largest repeated part in integer partitions, The Ramanujan Journal 25/2 (2011), 229-246. Preprint: [pdf]
  58. The number of spanning trees in self-similar graphs, Annals of Combinatorics 15/2 (2011), 355-380; with E. Teufl. Preprint: [pdf]
  59. Unicyclic graphs with large energy, Linear Algebra and its Applications 435/6 (2011), 1399-1414; with E. O. D. Andriantiana.
  60. Unfair Permutations, European Journal of Combinatorics 32 (2011), 1282-1298; with H. Prodinger and C. Schneider. Preprint: [pdf]
  61. The number of maximum matchings in a tree, Discrete Mathematics 311/21 (2011), 2512-2542; with C. Heuberger. Preprint available as report 2010-14: [pdf]
  62. Labeled trees, functions, and an algebraic identity, Electronic Journal of Combinatorics 18(1) (2011), P188 (5 pages); Preprint: [pdf]
  63. Separation of the maxima in samples of geometric random variables, Applicable Analysis and Discrete Mathematics 5/2 (2011), 271-282; with C. Brennan, A. Knopfmacher and T. Mansour.
  64. Asymptotic enumeration of extensional acyclic digraphs, Proceedings of the ANALCO12 Meeting on Analytic Algorithmics and Combinatorics, Kyoto, January 16, 2012, pp. 1-8. Preprint: [pdf]
  65. On the Wiener index of random trees, Discrete Mathematics 312/9 (2012), 1502-1511. Preprint: [pdf]
  66. Greedy trees, caterpillars, and Wiener-type graph invariants, MATCH Communications in Mathematical and in Computer Chemistry 68/1 (2012), 273-292; with N. S. Schmuck and H. Wang.
  67. Decomposing the hypercube Q_n into n isomorphic edge-disjoint trees, Discrete Mathematics 312/10 (2012), 1819-1822; with M. Wild. Preprint: [pdf]
  68. Additive tree functionals with small toll functions and subtrees of random trees, Proceedings of the 23rd International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms, Montreal, June 18-22, 2012, pp. 67-80. Preprint: [pdf]
  69. Energy Bounds for Graphs with Fixed Cyclomatic Number, MATCH Communications in Mathematical and in Computer Chemistry 68/3 (2012), 661-674.
  70. The matching energy of a graph, Discrete Applied Mathematics 160/15 (2012), 2177-2187; with I. Gutman. Preprint: [pdf]
  71. Analysis of Parameters of Trees Corresponding to Huffman Codes and Sums of Unit Fractions, Proceedings of the ANALCO13 Meeting on Analytic Algorithmics and Combinatorics, New Orleans, January 6, 2013; with C. Heuberger and D. Krenn.

Accepted for publication

  1. Asymptotic enumeration of extensional acyclic digraphs (full version), accepted for publication in Algorithmica. Preprint: [pdf]
  2. Enumeration of highly balanced trees, accepted for publication in Ars Combinatoria. Preprint: [pdf]
  3. A note on the number of dominating sets of a graph, accepted for publication in Utilitas Mathematica. Preprint: [pdf]
  4. Free Lamplighter Groups and a Question of Atiyah, accepted for publication in the American Journal of Mathematics; with F. Lehner. Preprint: [pdf]
  5. On sums of distinct odd squares arising from a class of totally symmetric plane partitions, accepted for publication in Bulletin Mathématique de la Société des Sciences Mathématiques de Roumanie; with A. Blecher, A. Knopfmacher and F. Luca. Preprint: [pdf]
  6. Distance-based graph invariants of trees and the Harary index, accepted for publication in FILOMAT; with H. Wang and X. Zhang. Preprint: [pdf]


  1. The number of cones generated by a Multiresolution Analysis with a sequence of LULU operators; with D. Laurie and C. Rohwer. Preprint: [pdf]
  2. A general asymptotic scheme for moments of partition statistics; with P. J. Grabner and A. Knopfmacher. Preprint: [pdf]
  3. Indistinguishable trees and graphs; with H. Wang. Preprint: [pdf]
  4. Bootstrapping and double-exponential limit laws; with H. Prodinger. Preprint: [pdf]
  5. On the local and global means of subtree orders; with H. Wang. Preprint: [pdf]
  6. Coupon collecting and transversals of hypergraphs; with M. Wild, S. Janson and D. Laurie. Preprint: [pdf]
  7. Greedy trees, subtrees and antichains; with E. O. D. Andriantiana and H. Wang. Preprint: [pdf]
  8. Hitting Times, Cover Cost, and the Wiener Index of a Tree; with A. Georgakopoulos. Preprint: [pdf]
  9. Central limit theorems for additive tree parameters. Preprint: [pdf]

Theses and other publications

  • An elementary proof of an inequality for convex lattice polygons: a paper I wrote when I was a masters student. Probably not important enough to be published in a high-quality journal, but I still like my proof. [pdf]
  • Ph.D. thesis: Graph-theoretical enumeration and digital expansions - an analytic approach [pdf]
  • Diploma thesis on applications of the Hardy-Littlewood-method: Anwendungen der Hardy-Littlewood-Methode - Partitionen und das Problem von Waring (German) [pdf]
  • "Fachbereichsarbeit" (small scientific work for the school leaving examination) on game theory: Spieltheorie (German) [pdf]
  • Seminar paper on finite simple groups: Einfache Gruppen sind kompliziert (German) [pdf]
  • Mathematical Olympiad

  • Combinatorics notes (English) [pdf]
  • Kombinatorik-Skriptum (German) [pdf]

  • Please note: All items are copyrighted either by the author or the publisher!