## Discrete Mathematics

The research group in discrete mathematics consists of Helmut Prodinger, Dimbinaina Ralaivaosaona, Stephan Wagner, and Marcel Wild. Their research interests cover various branches of discrete mathematics, including enumerative, probabilistic and analytic combinatorics, lattice theory and graph theory, discrete algorithms and the analysis of algorithms. Discrete mathematics has connections to various other branches of mathematics as well as other fields, such as computer science, chemistry and physics.

The group collaborates actively with other South African universities (Rhodes, UJ, Wits) as well as internationally, and it regularly hosts international guests from countries such as Austria, Belgium, Germany, Taiwan, and the United States of America.

There are plenty of opportunities for research in this diverse area, as is exhibited by the following list of recent publications:

- E.O.D. Andriantiana and S. Wagner, Spectral moments of trees with given degree sequence. Linear Algebra Appl. 439 (2013), 3980–4002.
- R. Balasubramanian, F. Luca and D. Ralaivaosaona, On the sum of the first n values of the Euler function. Acta Arith. 163 (2014), 199–201.
- A. Blecher, C. Brennan, A. Knopfmacher and H. Prodinger, The height and width of bargraphs. Discrete Appl. Math. 180 (2015), 36–44.
- C. Elsholtz, C. Heuberger and H. Prodinger, The number of Huffman codes, compact trees, and sums of unit fractions. IEEE Trans. Inform. Theory 59 (2013), 1065–1075.
- P. Grabner, A. Knopfmacher and S. Wagner, A general asymptotic scheme for the analysis of partition statistics. Combin. Probab. Comput. 23 (2014), 1057–1086.
- F. Lehner and S. Wagner, Free lamplighter groups and a question of Atiyah. Amer. J. Math. 135 (2013), 835–849.
- H. Prodinger, The box parameter for words and permutations. Cent. Eur. J. Math. 12 (2014), 167–174.
- H. Prodinger and R. Tauraso, New multiple harmonic sum identities. Electron. J. Combin. 21 (2014), Paper 2.43, 14 pp.
- D. Ralaivaosaona, On the distribution of multiplicities in integer partitions. Ann. Comb. 16 (2012), 871–889.
- M. Wild, Counting or producing all fixed cardinality transversals. Algorithmica 69 (2014), 117–129.
- M. Wild, S. Janson, S. Wagner and D. Laurie, Coupon collecting and transversals of hypergraphs. Discrete Math. Theor. Comput. Sci. 15 (2013), 259–270.
- M. Wild, Output-polynomial enumeration of all fixed-cardinality ideals of a poset, respectively all fixed-cardinality subtrees of a tree. Order 31 (2014), 121–135.