Critique of Hirsch's citation index: a combinatorial Fermi problem

The h-index was introduced by the physicist J.E. Hirsch in 2005 as measure of a researcher's productivity. We consider the "combinatorial Fermi problem" of estimating h given the citation count. Using the Euler-Gauss identity for integer partitions, we compute confidence intervals. An asymptotic theorem about Durfee squares, due to E.R. Canfield-S. Corteel-C.D. Savage from 1998, is reinterpreted as the rule of thumb h=0.54 x (citations)^{1/2}. We compare these intervals and the rule of thumb to empirical data (primarily using mathematicians).Comment: 10 pages + 3 page appendix; 2 figure

Tree-like properties of cycle factorizations

We provide a bijection between the set of factorizations, that is, ordered (n-1)-tuples of transpositions in ${\mathcal S}_{n}$ whose product is (12...n), and labelled trees on $n$ vertices. We prove a refinement of a theorem of D\'{e}nes that establishes new tree-like properties of factorizations. In particular, we show that a certain class of transpositions of a factorization correspond naturally under our bijection to leaf edges of a tree. Moreover, we give a generalization of this fact.Comment: 10 pages, 3 figure