The Hurwitz graph has as its vertices the maximal chains in the lattice of non-crossing partitions, with an edge between two chains which differ at exactly one place. Adin and Roichman introduced an order on this graph by choosing a base element and showed that the maximal elements are counted by the Catalan numbers. We show that this set of maximal elements is in natural bijection with non-crossing partitions so that the graph structure corresponds to that of the permutahedron, restricted to non-crossing partitions. We use this to compute the diameter of the graph of maximal elements. We also briefly consider the graph obtained by identifying maximal chains with minimal factorizations of a full cycle into transpositions in the symmetric groups and quotienting by commutation relations.
This publication proposes a definition and a classification of agile software development approaches and analyses ten software development methods that can be characterized as being "agile" against the defined criterion.
P. Abrahamsson, O. Salo, Jussi Ronkainen et al.· arXiv.org· 727 citations· ⚡54
The study shows that agile practices improve both informal and formal communication, but indicates that, in larger development situations involving multiple external stakeholders, a mismatch of adequate communication mechanisms can sometimes even hinder the communication.
M. Pikkarainen, Jukka Haikara, O. Salo et al.· Empirical Software Engineeri...· 401 citations· ⚡48
The results indicate that software engineering work practices are chosen opportunistically, adapted and configured to provide value under the constrains imposed by the startup context.
Nicolò Paternoster, Carmine Giardino, M. Unterkalmsteiner et al.· Information and Software Tec...· 394 citations· ⚡54
The perception of the impact of agile methods is predominantly positive, and several challenge areas were discovered, but based on this study, agile methods are here to stay.
M. Laanti, O. Salo, P. Abrahamsson· Information and Software Tec...· 260 citations· ⚡20
Related blog posts
MIT News · Artificial Intelligence· news.mit.eduOct 15, 2026
A new computational approach reveals how cells communicate to assemble into tissues. This could accelerate stem cell engineering, improve disease models, and inform therapies.
Microsoft Research Blog· microsoft.comOct 15, 2026
Zero-knowledge proofs can verify computing results without rerunning workloads or exposing sensitive data. Magnetar helps bring them into the mainstream with support for standard programming languages, major speed gains, and quantum-resistant security. The post Proof-based general-purpose computing with Magnetar appeared first on Microsoft Research.
MIT News · Artificial Intelligence· news.mit.eduOct 8, 2026
