Publications up to 2014

Scientific papers

2005

1. Extremal Problems for Topological Indices in Combinatorial Chemistry, Journal of Computational Biology 12/7 (2005), 1004-1013; with R.F. Tichy. Preprint: [pdf]

2006

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]

2007

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.

2008

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]

2009

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. Preprint: [pdf]
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 E. Czabarka and L. Székely. 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]

2010

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: Mathematical and Theoretical 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) (2010), R137 (9 pages); 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]

2011

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. Preprint: [pdf]
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. Preprint: [pdf]
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.

2012

64. Asymptotic enumeration of extensional acyclic digraphs, Proceedings of the ANALCO12 Meeting on Analytic Algorithmics and Combinatorics, Kyoto, January 16, 2012, pp. 1-8.
65. On the Wiener index of random trees, Discrete Mathematics 312/9 (2012), 1502-1511. Preprint: [pdf]
66. Successions in words and compositions, Annals of Combinatorics 16/2 (2012), 277-287; with A. Knopfmacher and A. Munagi. Preprint: [pdf]
67. 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.
68. Decomposing the hypercube Q_n into n isomorphic edge-disjoint trees, Discrete Mathematics 312/10 (2012), 1819-1822; with M. Wild. Preprint: [pdf]
69. Additive tree functionals with small toll functions and subtrees of random trees, Proceedings of the 23rd International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms, Montreal, June 18-22, 2012, pp. 67-80.
70. Energy Bounds for Graphs with Fixed Cyclomatic Number, MATCH Communications in Mathematical and in Computer Chemistry 68/3 (2012), 661-674.
71. The matching energy of a graph, Discrete Applied Mathematics 160/15 (2012), 2177-2187; with I. Gutman. Preprint: [pdf]

2013

72. 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, pp. 33-42; with C. Heuberger and D. Krenn.
73. On sums of distinct odd squares arising from a class of totally symmetric plane partitions, Bulletin Mathématique de la Société des Sciences Mathématiques de Roumanie 56(104)/2 (2013), 163-171; with A. Blecher, A. Knopfmacher and F. Luca. Preprint: [pdf]
74. Free Lamplighter Groups and a Question of Atiyah, American Journal of Mathematics 135/3 (2013), 835-849; with F. Lehner. Preprint: [pdf]
75. Distance-based graph invariants of trees and the Harary index, FILOMAT 27/1 (2013), 41-50; with H. Wang and X. Zhang. Preprint: [pdf]
76. Asymptotic enumeration of extensional acyclic digraphs (full version of 64.), Algorithmica 66/4 (2013), 829-847. Preprint: [pdf]
77. Greedy trees, subtrees and antichains, Electronic Journal of Combinatorics 20/3 (2013), P28 (25 pages); with E. O. D. Andriantiana and H. Wang.
78. Coupon collecting and transversals of hypergraphs, Discrete Mathematics and Theoretical Computer Science 15/2 (2013), 259-270; with M. Wild, S. Janson and D. Laurie. Preprint: [pdf]
79. The number of fixed points of Wilf's partition involution, Electronic Journal of Combinatorics 20/4 (2013), P13 (7 pages).
80. A note on the number of dominating sets of a graph, Utilitas Mathematica 92 (2013), 25-31. Preprint: [pdf]
81. Spectral moments of trees with given degree sequence, Linear Algebra and its Applications 439 (2013), 3980-4002; with E. O. D. Andriantiana. Preprint: [pdf]

2014

82. Set partition asymptotics and a conjecture of Gould and Quaintance, Journal of Mathematical Analysis and Applications 416/2 (2014), 672-682; with W. Asakly, A. Blecher, C. Brennan, A. Knopfmacher and T. Mansour. Preprint: [pdf]
83. Enumeration of highly balanced trees, Ars Combinatoria 114 (2014), 15-32. Preprint: [pdf]
84. Graphs with maximal Hosoya index and minimal Merrifield-Simmons index, Discrete Mathematics 329 (2014), 77-87; with Z. Zhu, C. Yuan and E. O. D. Andriantiana. Preprint: [pdf]
85. On the number of multi-base representations of an integer, Proceedings of the 25th International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms, Paris, June 16-20, 2014, pp. 229-240; with D. Krenn and D. Ralaivaosaona.
86. The number of compositions into powers of b, Proceedings of the 25th International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms, Paris, June 16-20, 2014, pp. 241-252; with D. Krenn.
87. Counting glycans revisited, Journal of Mathematical Biology 69/4 (2014), 799-816; with S. Böcker. Preprint: [pdf]
88. Indistinguishable trees and graphs, Graphs and Combinatorics 30/6 (2014), 1593-1605; with H. Wang. Preprint: [pdf]
89. A general asymptotic scheme for the analysis of partition statistics, Combinatorics, Probability and Computing 23/6 (2014), 1057-1086; with P. J. Grabner and A. Knopfmacher. Preprint: [pdf]
90. Uniform spanning trees on Sierpinski graphs, ALEA - Latin American Journal of Probability and Mathematical Statistics 11 (2014), 737-780; with M. Shinoda and E. Teufl. Preprint: [pdf]

Book chapter

Theses and other publications

Mathematical Olympiad