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All links should be available for free to the public or with UConn net ID

Student expository presentations on papers during week 8 and 9 (notes and slides)

• Paper presentation on Stanley’s Promotion and evacuation by A. Rumbolt

• Paper presentation on Britz and Fomin’s Finite posets and ferrers shapes by B. Drucker

• Paper presentation on Early’s Chain lengths in the Tamari lattice and Lim–Zhang’s Previously unknown parts of the Greene-Kleitman partition for the Tamari lattice by R. Silver

• Paper presentation on Bédard’s On commutation classes of reduced words in Weyl groups by E. Garcia

  • presentation notes and slides
  • GeoGebra link
  • An example from the paper

Relevant to both PROBLEM I and II

Britz and Fomin: Greene, Kleitman, Fomin invariants of a poset

• Several sections from Thomas Britz and Sergey Fomin. Finite posets and ferrers shapes a survey on Greene-Kleitman invariants 1999

• Errata and side notes written by Darij Grinberg (read-only link), I have sent you all invitations to edit — please add to it if you see typos

• Supporting materials:
  • Sagan textbook chapter 3 and 4
  • Jeremy Martin Lecture notes on algebraic combinatorics 2020, the first two chapters are on posets and lattices, properties for graded and distributive lattices, etc.
  • Curtis Greene. An extension of Schenstead’s Theorem. 1974
  • Curtis Greene and Daniel J Kleitman. The structure of Sperner k-Families. 1976
  • 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.
  • Lecture videos from Georgia Tech Math 3012. Lecture 14 – Posets: Mirsky’s and Dilworth’s Theorems, slides
• Videos and slides:
  • Videos and slides by Vienno

Stanley: Promotion and evacuation

• Richard Stanley. Promotion and evacuation 2009

• Supporting materials:

  • Sagan textbook chapter 3 and 4
  • My notes about page 4–6 of the paper

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Most relevant to PROBLEM I

LLPS: Localized version of Greene’s theorem

• Section 1, 2, and 9 (or more sections) of Lewis, Lyu, Pylyavskyy, Sen. Scaling limit of soliton lengths in a multicolorbox-ball system.

• Other papers:

  • Atsuo Kuniba and Hanbaek Lyu Large Deviations and One-Sided Scaling Limit of Randomized Multicolor Box-Ball System 2019

Fukuda: Box-ball systems and RSK

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

• Links to survey on box-ball system:

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

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Papers most relevant to PROBLEM II

Bedard: Commutation classes

• Focus on the combinatorial aspects, for type A Coxeter group (symmetric group) — you may ignore some algebraic concepts Robert Bedard On commutation classes of reduced words in Weyl groups. 1999
  • You can meet with me for a crash course on concepts from Coxeter groups which haven’t been discussed yet

Labbe and Lange: c-singletons

• Jean-Philippe Labbe and Carsten Lange. Cambrian acyclic domains: counting c-singletons. 2018 published version (2020) in a journal called Order

• Supporting (earlier) papers:
  • Christophe Hohlweg and Carsten Lange Realizations of the associahedron and cyclohedron. 2005, the c-singletons were discussed but are just called singletons here
  • Christophe Hohlweg, Carsten Lange, and Hugh Thomas Permutahedra and generalized associahedra. 2007, the first time the term c-singletons were introduced

Greene-Kleitman invariant of the Tamari lattice

• Present both papers on the Greene-Kleitman invariant of the Tamari lattice
  • Edward Early. Chain lengths in the Tamari lattice. 2003, 8 pages. Some of the computation for small n is incorrect (like for the Tamari lattice with 42 elements)
    • Fig 1 with largest union of two chains highlighted
  • Raphael-Joel Lim and Mark Zhang. Previously unknown parts of the Greene-Kleitman partition for the Tamari lattice. 2008, 19 pages. Please create a list of typos, so we can fix the typos before posting the paper in public.
• Supporting materials:
  • (book) Richard Stanley Catalan Numbers 2015. Checkout or request an electronic copy from your library’s MathSciNet page.
  • Draft of the book: Richard Stanley Catalan Addendum 2013
  • The materials about Greene-Kleitman partition under the Britz and Fomin’s survey paper

Elnitsky: Rhombic tilings and commutation classs

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