Weeks -4 to 0

- Studied James Abello's paper on Visibility Graphs of Staircase Polygons and the Weak Bruhat Order;I: From Visibility Graohs to Maximal Chains

Week 1

- Studied basic properties of staircase polygons and their visibility graphs(persistent graphs).

- Got a better understanding of how to build persistent graphs.

- For different examples of persistent matrices tried to built a staircase polygon P such that the visibility graph of P, Vis(P), was precisely the persistent matrix I started with.

Week 2

- Continued working with examples of persistent matrices, M, trying to construct a staircase polygon P such that Vis(P) = M.

- Studied more deeply Balanced Tableaus. Learned more about the information encoded in them, and how to use it to reconstruct staircase polygon P given Vis(P).

-Project Presentation

Week 3

- Continued working with examples of persistent matrices, M, trying to construct a staircase polygon P such that Vis(P) = M. This time using basic algebra to decode the information in the corresponding balanced tableau

- Using the information in the first column and first diagonal of the abello tableau to construct Vis(P).

Week 4

- Going from an Abello tableau to its corresponding clique (persistent matrix where all entries are ones) by deleting the row and column of the blocking vertex.Then constructing Vis(P) of that clique using algebra on the first diagonal and the first column.

- Worked on the proof for a factor(persistent graph with only one blocking vertex).

Week 5

- Started working with examples of persistent graphs with more than one blocking vertex.

- Studied the current algorithm for constructing the Abello tableau of such persistent graphs.

- Started trying to come up for a construction method to reconstruct the staircase polygon of such visibility graphs.

Week 6

- Continued working on coming up for a construction method to reconstruct the staircase polygon of such visibility graphs.

Week 7

- Continued working on coming up for a construction method to reconstruct the staircase polygon of such visibility graphs.

-Results Presentation

- Worked on an alternate proof for a factor.

Week 8

- Wrote up final report on my project.

- Prepared poster for RISE program.