(Please refresh page at each visit!)

Commutation classes, rhombic tilings, AR quiver

• Serge Elnitsky Rhombic tilings of polygons and classes of reduced words in Coxeter groups. 1994

• Robert Bedard On Commutation Classes of Reduced Words in Weyl Groups. (1999)

Friendly Introduction to Cambrian lattices, taken from N. Reading’s papers and slides

• 2012 Survey article by N. Reading From the Tamari lattice to Cambrian lattices and beyond

• 2004 Slides by N. Reading Cambrian lattices and generalized associahedra

Papers on Cambrian lattices

• Nathan Reading. Clusters, Coxeter-sortable elements and noncrossing partitions. 2005

Greene-Kleitman invariants for Tamari lattices

• Edward Early. Chain lengths in the Tamari lattice. 2003, 8 pages

• Raphael-Joel Lim and Mark Zhang. Previously unknown parts of the Greene-Kleitman partition for the Tamari lattice. 2008, 19 pages

Catalan numbers

• Andrew M. Odlyzko and Herbert S. Wilf The Editor’s Corner: n Coins in a Fountain 1988, needs UConn NetID

Greene, Kleitman, Fomin invariants of a poset

(Links are free to the public)

• Curtis Greene. An extension of Schenstead’s Theorem. 1974

• Curtis Greene and Daniel J Kleitman. The structure of Sperner k-Families

• C. Schensted. Longest increasing and decreasing subsequences. 1961
  • Note: The same proof is reproduced in textbooks Stanley’s EC v2 appendix and Sagan’s Symmetric Group Chapter 3.
• Thomas Britz and Sergey Fomin. Finite posets and Ferrers shapes, a survey on Greene-Kleitman invariants arxiv version 1999

Dilworth’s theorem and its dual

• Lecture videos from Georgia Tech Math 3012. Lecture 14 – Posets: Mirsky’s and Dilworth’s Theorems, slides

• Go to your institution (or UConn)’s library page, look for MathSciNet, search for then download the article A Proof of Dilworth’s Chain Decomposition Theorem by Fred Galvin from 1994.

BBS Soliton partition

• Atsuo Kuniba and Hanbaek Lyu Large Deviations and One-Sided Scaling Limit of Randomized Multicolor Box-Ball System 2019 — discusses Schensted row insertion row insertion and column insertion, and how to find lengths of BBS shape using a finite-capacity carrier algorithm

• Joel B Lewis. Blog post a localized version of Greene’s Theorem. 2019

• Lewis, Lyu, Pylyavskyy, Sen. Scaling limit of soliton lengths in a multicolorbox-ball system. The most relevant parts for us are Section 1,2, and 9.

• Kaori Fukuda. Box-ball systems and Robinson-Schensted-Knuth correspondence arxiv, published version (2004)

• Rei Inoue, Atsuo Kuniba, Taichiro Takagi. Integrable structure of box-ball systems: crystal, Bethe ansatz, ultradiscretization and tropical geometry 2011, a 73 pp. survey arxiv 2011, published version — use UConn ID to download

• Slides Randomized box-ball systems, limit shape of soliton distributions and thermodynamic Bethe ansatz

Textbooks

• This is not the Sagan book we normally use Bruce Sagan Combinatorics: The Art of Counting 2020 preliminary version

• Good reference for posets Jeremy Martin Lecture notes on algebraic combinatorics 2020, the first two chapters are on posets and lattices, properties for graded and distributive lattices, etc.

• Possible reference for permutations, permutation statistics like descents, pattern avoidance, etc: Miklos Bona Combinatorics of permutations, you can find a link to read the e-book via UConn library or your school library

• Per Alexandersson Symmetric functions catalogue HTML writing on topics like partitions, tableaux, RSK, their connection to the weak order

• Richard Stanley Graduate textbook Enumerative Combinatorics Volume 1, 2nd ed , Chapters 1–4

• Richard Stanley Undergraduate textbook Algebraic Combinatorics 2nd ed. Free download with UConn NetID via this link, you can also go to MathSciNet through your institution library to get it (if your institution has a copy)

• Geometric Combinatorics edited by Ezra Miller, Victor Reiner, and Bernd Strumfels, IAS/Park City Mathematics Series, requires UConn NetID

Errata

• Errata for the 2nd edition of Bruce Sagan’s The Symmetric Group 2nd ed

Misc

• LivingProof: Stories of Resilience Along the Mathematical Journey