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Lecture notes

• Sage Images of the right weak order on the symmetric group with 5! elements, with 6! elements

• MathSciNet and BibTeX guide and tasks

Problem 1 notes

• Problem 1 notes, part 1 (last updated: 5pm Thurs, June 11), permutations, Greene’s theorem, BBS soliton version of Greene’s theorem; REU Exercises 1 (done), 2, 3 (done), and 4. The BBS here is the opposite of what we adopt.

• Problem 1 notes, part 2 (last updated: 7pm Wed, June 3), Hasse diagrams, inversion poset, Greene-Kleitman invariant/ partition. Update: Part 2 question does not seem to work naturally for inversion poset. No REU Exercise here. The BBS here is the opposite of what we adopt.

• Problem 1 notes, part 3 (last updated: Mon July 6), Fukuda convention for BBS. Sagan’s Chapter 3 RS algorithm, conjectures about soliton content soliton decomposition, standard Young tableau, and RS insertion tableau; REU Exercises 5,6a, 6b, and 7. Don’t use the notation used here for localized lambda.

• Problem 1 notes, part 3b (last updated: Mon July 6) New Conjectures 5,6,7 and propositions about Knuth moves of the first and second kind. Conjecture 6 is called Theorem 1. Adopt the notation used here for descents, localized lambda, etc.

• Problem 1 notes, backward RSK (last updated: Mon July 6), backward RSK, backward row reading word, conjecture about “backward” soliton decomposition, evacuation, dihedral group on the symmetries of a square; REU Exercise 15

• Problem 1 cargo-train or M-carrier algorithm reu20prob1train.pdf

Problem 2 notes

• python file containing Greene-Kleitman partition data for Tamari lattice and bipartite (1,3,5,…,2,4,6,…)-Cambrian lattice up to n=8 (S9) and halfway (…,5,4,3,2,1,…,n-1,n)-Cambrian lattice

• Problem 2 notes, part 1 (last updated: June 15), Tamari lattice, eta map, 312 avoiding permutations, 132 avoiding permutations, Greene-Kleitman invariant of the Tamari lattice; REU Exercise 8 (everyone should be able to do this proof)

• Problem 2 notes, part 2 (updated Tues, June 16), Cambrian lattice, bipartite Cambrian lattice; REU Exercise 9, 10

• Problem 2 notes, words, c-sortable words etc (updated Thurs June 25) Coxeter group, reduced words, c-sorting words, c-sortable elements; REU Exercise 11 — the same notes but starting from page 5, for people who are familiar with reduced words in type A Coxeter groups: c-sorting words and c-sortable words

• Problem 2 notes, commutation class etc (updated Thurs June 22) commutation class, maximum-length chains of c-sortable words; REU Exercise 12, 13, 14

• Problem 2 notes, tilings and heaps (updated Mon June 22) Interpretation of commutation classes as rhombic tilings of Elnitsky polygons and heaps

• Problem 2 notes, part 3, Cambrian lattice realizations on plabic graphs

• Notes on how to go back and forth between Coxeter elements and orientations of a type A Dynkin quiver

Schedule

All meetings are in Eastern Time.

CURRENT: Week 10 (July 27 – 31, 2020)

• Mon
  • (I have a meeting starting at noon (MRC))
  • 2pm Eli’s presentation
  • 6pm Office hour meeting (Ben)
• Tue
  • Optional office hour appointments
  • Office hour meeting at noon (Rose)
  • (I have a meeting starting at 3pm)
• Wed
  • Optional office hour appointments
• Thurs

  • Math REU Conference

  • 2pm Karin Baur’s frieze talk at WinCom

• Fri
  • 2pm all-reu meeting

Past: Week 9 (July 20 – 24, 2020)

• Mon
  • (FPSAC 10-11:30am talks, 11:30 coffee break, 12-1pm Remembrances of Ron Graham)
  • (I have a meeting starting at 1:30pm — Computer Algebra)
• Tues
  • Optional office hours
  • (I have IBL webinar starting at 1pm)
  • 2pm all-REU meeting Tues presentations
  • Meeting after
• Wed
  • (FPSAC 10-11:30am talks, 11:30 coffee break, 6-7:30pm Poster Session III)
  • Meeting before Eli’s presentation? Optional office hours
  • 1pm I meet with Aubrey (Ben and Eli can join)
  • TBA Eli paper presentation
• Thurs
  • Optional office hours

  • (I have a meeting at noon (topology) and another starting at 3pm)

  • 5:15pm Optional Thurs mafia-like games at Minneapolis REU
• Fri
  • (FPSAC 10-11:30am talks, 11:30 concluding remarks and awards)

  • TBA present conference talks with live audience

  • 5:15pm Optional Fri mafia-like games at Minneapolis REU

Past: Week 8 (July 13 – 17, 2020)

• Mon
  • Optional office hour meetings
  • Group meeting
  • (I have another meeting at 3:30-4:30pm)
• Tue
  • Optional office hour appointments
  • 1pm Meeting at Ben’s WebEx room to listen to Aubrey and Ben practice
  • 2pm all-REU presentations
  • (I have a meeting at 4pm)
  • Optional office hour appointments
• Wed
  • (I am going to FPSAC + meeting 10-12:30pm)
  • Ben 1pm present paper
  • (I have a meeting 3-7pm)
  • 5:15pm Social event organized by Esther with Minneapolis REU, around one hour or less (Optional, but if Rose or Ben changes their mind please tell me so I can let Esther know)
• Thurs
  • 12:30pm Aubrey present paper
  • Optional office hour appointments
  • (I have a meeting 8pm)
• Fri
  • Optional office hour appointments
  • 12pm Rose present (Eli present next week)
  • 2pm REU Seminar (Please don’t leave the seminar until Luke ends the virtual room)
  • 3pm Optional Minneapolis professional development event on growth mindset
  • (Rose has appt at 4pm)
  • (6-8pm FPSAC, coffee break theme: platform exploration)

• MathSciNet and BibTeX pre-presentation tasks due one day before your presentation — don’t submit this too early

Past: Week 7 (July 6 – 10, 2020)

• Mon
  • Before 2pm: optional office hour meetings (by appointments)
  • 12:30pm Meeting with Ben
  • 2:30pm Meet as a group
• Tue
  • 2pm all-REU presentations
  • 3-5pm optional office hour meetings (by appointments)
• Wed
  • 12-3pm optional office hour meetings (by appointments)
  • 12pm Meeting with Eli
  • 2pm Meeting with Rose
• Thurs
  • 12:30pm Group Meeting, lecture Problem II part 3 notes.
• Fri
  • 12:30pm Group meeting
  • 2pm REU Seminar (E. Meehan)
  • 3pm Optional Minneapolis professional development event (grad school panel)
  • 4:15pm (tentative) If needed, have a second group meeting to discuss Tues presentations

PRiME is the Math History REU run at Pomona College. Their REU seminar talks (Tues and Thurs 1pm Pacific/4pm Eastern Time until July 21) are open to the general public. Speaker series schedule and link

Past: Week 6 (June 29 – July 3, 2020)

• Mon
  • Ben and Eli announce that slides draft are ready around 2pm
  • Meet with everyone 3pm I am available if you want to meet with me before 2pm or after 4pm
• Tue
  • Meet with everyone 1pm before presentations
  • 2pm all-REU progress report presentations
  • 4pm (or 15 minutes after the end of the presentations, whichever is EARLIER) Meeting, short intro to MathSciNet, Google Scholar and BibTeX

• Wed optional Permutation Pattern conference, no group meeting with me

• Thurs 2pm Combinatorics group meeting, discuss new conjectures from PDF Problem 1 notes, part 3b

• Fri
  • 9am–12pm optional office hour meetings (by appointments)
  • 2pm REU Seminar (D. Labardini Fragoso)
  • 4:15pm Combinatorics group meeting, discuss next week’s Tues presentation

• June 30 - July 1 Permutation Pattern conference

• MathSciNet and BibTeX beginner tasks due by the end of this week

Past: Week 5 (June 22 – 26, 2020)

• Mon
  • Aubrey and Rose share slides around 2pm
  • Meet with everyone 3pm: Discuss sides, discuss Rose’s notes on Problem 2, part 2. Lecture rhombic tilings
• Tue
  • Meet with everyone 1pm before presentations
  • 2pm all-REU progress report presentations
  • Meet with everyone after presentations 4:10pm. Progress report.

• Wed 1pm optional GOCC talk, no scheduled meeting with me

• Thurs 2pm Combinatorics group meeting. Lecture on evacuation, backward RSK, and dihedral group on symmetries of a square (see PDF Problem 2 notes, backward RSK)

• Fri
  • 2pm REU Seminar
  • 4pm Combinatorics group meeting. Ben’s HPC presentations, discuss next week’s talk, Rose’s k-swaps, and paper presentations

Past: Week 4 (June 15 – 19, 2020)

• Mon
  • Share slides and plans/notes with me by 3pm
  • Meet with me at 5pm. Finish lecture Problem 2 notes, part 2.
• Tue
  • 2pm all-REU progress report presentations
  • 3:50pm Combinatorics group meeting afterwards. Start lecture “Problem 2 notes, words, c-sortable words etc” up to Sec 2.9 Coxeter element
• Wed No scheduled meeting with me
• Thurs 2pm Combinatorics group meeting. Finish lecture “Problem 2 notes, words, c-sortable words etc”.
• Fri
  • 2pm REU Seminar
  • 3:30 Combinatorics group meeting. Lecture “Problem 2 notes, commutation class etc”

Past: Week 3 (June 8 – 12, 2020)

• Mon
  • Share slides and plans/notes with me by 3:30pm
  • Meet with me at 4:15pm. Discuss slides. Start lecture Problem 2 notes, part 1, up to Exercise 8.
• Tues
  • 2pm all-REU progress report presentations
  • No Combinatorics group meeting afterwards
• Wed No group meeting
• Thurs 2pm Combinatorics group meeting, finish Problem 2 notes, part 1. Give just the overview of Problem 2 notes, part 2.
• Fri
  • 2pm REU Seminar
  • 3:30 Combinatorics group meeting after

Past: Week 2 (June 1 – 5, 2020)

• Mon 2pm Combinatorics group meeting
• Tues 2pm all-REU meeting: progress report presentations. Combinatorics group meeting at 4pm.
• Wed You can start meeting at 2pm. I will join you later than usual, at 4pm. Lecture on Sagan’s Chapter 3 and Problem 1 part 3 (up to Sec 1.9).
• Thurs Combinatorics group meeting at 2pm. Will continue lecture on Problem 1 part 3 (pattern avoidance)
• Fri 2pm REU Seminar (speaker: Greg Muller from University of Oklahoma). Group meeting after (discuss next week’s presentation). Finish Problem 1 notes, part 3.

Past: Week 1 (May 26 – 29, 2020)

• Tues
  • 1pm all-REU Meet and greet (Luke Roger will send an email with the link)
  • 2pm Combinatorics group meeting: Lecture on Problem 1 part 1, up to Sec 1.4

• Wed 2pm Combinatorics group meeting: Students share progress to exercises + lecture Sec 1.5 (use usual virtual meeting link for Combinatorics)

• Thurs 2pm Combinatorics group meeting: Students share progress to exercises + lecture on Problem 1, part 2

• Fri 2pm Combinatorics group meeting: progress reports (Exercise 1 and Exercise 3) + lecture on RSK algorithm