## SSL Minutes

27 Feb 2001

Dominic and Rachel

**Note: I apologize in advance if I did not understand/record your main points you presented on Tuesday. If I missed anthing, misinterpreted what you said, or said something you did not say, please send me a note explaining the mistake or what you would like changed.

Hal will bring the beverage for Thursday's meeting.

Kekule structures from benzene molecules are related to Hal's interest in nanotubes and their possible tilings. A benzene molecule yields 2 Kekule structures (2 perfect matchings).

Question: Do we want our meeting minutes in postscript or pdf?

We will collect the minutes of all our meetings into a separate file. It is a good idea to send out both rough and revised versions of the minutes. When revising minutes, though, send the addenda/errata and the full revision in separate messages. That way, people can immediately see what has changed from the rough draft, but also have a revised text to refer back to at a later date. Also, multiple revisions are allowed and even encouraged. Everyone can suggest changes, and the authors implement them.

Additionally people questioned how "good" should the minutes be? and should there be a difference in the quality of notes sent by Tuesday notetakers vs Thursday notetakers? The revision version of the notes should be as 'perfect' as we can get the notes, and that's how 'good' the notes should be!

We went around the room, and each person conducted the meeting for roughly five minutes.

Geir: Nothing in particular. Not so much interested in the Arctic Circle, but in the number of matching permutation matrices. Interested in Baxter Permutations. What are they?

**Homework assignment for Thursday: Find a definition of Baxter Permutations.

Abe: Concerned about the number of ways to join 1 & 2, 3 & 4, etc. Also interested in symmetries in blue/green paths used to join these numbers. Boytcho was also interested and had been working on these blue/green path symmetries as well.

Pavle: Interested in the tilings of a square (or diamond, depending on which way you look at it). Presented a few pictures to explain his ideas, and showed how he has been spending his time.

Dominic: Wondered why David Robbins tried to make his data look similar to Pascal's Triangle. It turns out Pascal's triangle can also be applied to Aztec Diamonds. Other than that, Dom has been spending most of his time reading the articles and learning computer language.

Nick: Opted to speak at the end of the meeting because his talk would probably take longer than 5 minutes. However, we did not have enough time at the end of the meeting for him to talk.

Joel: Has mostly been catching up. Interested in overlapping domino matchings, blue/green paths, and how they are related to superpositions of domino tilings.

Michael: Ceded his time to others.

Dan: Wonders if there's a good source to learn Java. Computer-literate people suggested taking Computer Science 368 here at the university. Also, perhaps read through a few Java books, and within a few minutes of reading, you should be able to tell if it fits your learning style.

Winston: Interested if there's research done in the tilings of any regular polygon. Jim showed the example of a regular octagon (edge length 1) being tiled by 2 squares and 4 non-square rhombi. There is no known way to tile a 2n-gon (I think). Also, Jim introduced ribbon tiles. There are two 2-ribbons. One looks like a horizontal domino. The other looks like a vertical domino. There are four 3-ribbons. They look like the Tetris pieces generated when one can only move eastward and northward. How many ways are there to tile a figure using ribbon tiles?

Rachel: Interested in having brainstorming sessions. Also concerned about what/how an SSLer without mathematical sophistication can contribute. Interested in having a study session, which could be facilitated if all members could post a list of their free times. The group decided it could be beneficial if a member specialized in one specific area, so even if he/she did not have mathematical or computer sophistication, he/she could teach others about his/her area of expertise.

Boytcho: I apologize, but I'm not exactly sure how to put this into words. He looked at all the different tilings of an order-2 Aztec Diamond. Then he translated each tiling into a 4-by-matrix. Then he transformed this into an arrangement of green and blue lines, assigned a "weight" to each colored segment, and looked for patterns.

Kristin: Has spent her time learning about computers. Interested in tiling different polygons. Can we use other shapes (which ones?) for tilings? When do you know if a region is tilable? Jim explained the marriage lemma and its connection with tilable/untilable regions.

Hal: Comments on the ideas Boytcho presented. He represents Aztec Diamonds as huge arrays. Interested in how we can go from a Aztec Diamond to any other shape. Hal's time also ran out and he will be given time at the next meeting to finish his minutes.

Figures will be added in the revision to these notes.