Non-crossing partitions

Some (mostly on-line) resources

Introductory papers, Lecture notes and Survey papers:

• H. Muehle, Noncrossing set partitions .
• B. Baumeister, K. Bux, F. Götze, D. Kielak, H. Krause, Non-crossing partitions.
• G. Kreweras, On the noncrossing partitions of a cycle.
• J. McCammond, Noncrossing Partitions in Surprising Locations.
• H. Krause, Non-crossing partitions arising in representation theory.
• R. Speicher, Free probability theory and non-crossing partitions.

Non-crossing partition and root systems:

• V. Reiner, Non-crossing partitions for classical reflection groups .
• Drew Douglas Armstrong, Generalised noncrossing partitions and combinatorics of Coxeter groups , PhD thesis, Cornell University 2006.
• C. Athanasiadis, V. Reiner, Non-crossing partitions for the group D_n.
• C. Athanasiadis, T. Brady, C. Watt, Shellability of noncrossing partition lattices.
• T. Brady, C. Watt, Non-crossing partition lattices in finite real reflection groups.
• M. Rubey, C. Stump, Crossings and nestings in set partitions of classical types.
• R. Simion, Noncrosing partitions.

Some other results:

• Jang Soo Kim, New interpretations for non-crossing partitions of classical types.
• J. Rue, I. Sau, D. M. Thilikos, Asymptotic enoumeration of non-crossing partitions on surfaces.
• D. Armstrong, Generalised noncrossing partitions and combinatorics of Coxeter groups, PhD Thesis.
• R. P. Stanley, Parking functions and noncrossing partitions.
• N. Williams, Cataland, PhD Thesis, 2013

Non-crossing partitions and cluster algebras, associahedra, marked surfaces:

• S. Fomin, N. Reading, Root Systems and Generalized Associahedra, see p.57.
• N. Reading, Noncrossing partitions, clusters and the Coxeter plane.
• N. Reading, Clusters, Coxeter-sortable elements and noncrossing partitions.
• N. Reading, Chains in the noncrossing partition lattice.
• N. Reading, Noncrossing partitions and the shard intersection order.
• P. Biane, M. Josuat-Verges, Noncrossing partitions, Bruhat order and the cluster complex .
• C. Ingalls, H. Thomas, Noncrossing partitions and representations of quivers .
• N. Reading, Noncrossing partitions of a marked surface.
• L. Brestensky, N. Reading, Noncrossing partitions of an annulus.

Non-crossing and non-nesting:

• R. Mamede, A bijection between noncrosing and nonnesting partitions of types A and B.
• D. Amstrong, C. Stump, H. Thomas, A uniform bijection between noncrosing and nonnesting partitions.
• W. Chen, E. Deng, R. Du, R. Stanley, C. Yan, Crossings and nestings of matching and partitions.
• A. Fink, B. I. Giraldo, Bijections between noncrossing and nonnesting partitions for classical reflection groups.
• V. Reiner, Warm-up in type A: noncrossing, nonnesting partitions and associahedra.
• C. Athanasiadis, On noncrossing and nonnesting partitions for classicl reflection groups.

Presentations:

• H. Muehle, On noncrossing partitions .
• C. Stump, A bijection between non-crossing and non-nesting partitions of types A and B.

Webpages:

• Wikipedia page: Non-crossing partitions.
• Webpage: Resources and background Reading by Jon McCammond.
• Workshop: "Non-crossing partitions in representation theory" - abstracts and slides