# Determinants and Dodgson’s condensation

1. In Lecture 20 I sketched MacMahon’s proof for the enumeration of plane partitions, reducing it to an evaluation of a determinant built from one row of Pascal’s triangle. See the bottom of pg 90: http://math.sfsu.edu/federico/Clase/EC/LectureNotes/ardilaec20.pdf Was anyone able to prove

# Determinants and Dodgson’s condensation

1. In Lecture 20 I sketched MacMahon’s proof for the enumeration of plane partitions, reducing it to an evaluation of a determinant built from one row of Pascal’s triangle. See the bottom of pg 90: http://math.sfsu.edu/federico/Clase/EC/LectureNotes/ardilaec20.pdf Was anyone able to prove

# Literature on alternating sign matrices

Here are the very interesting and entertaining articles on alternating sign matrices that I promised: Bressoud and Propp’s “How the Alternating Sign Matrix Conjecture was solved”:   http://www.ams.org/notices/199906/fea-bressoud.pdf Propp’s “The many faces of alternating sign matrices”   http://arxiv.org/pdf/math/0208125v1.pdf Zeilberger’s proof:

# Literature on alternating sign matrices

Here are the very interesting and entertaining articles on alternating sign matrices that I promised: Bressoud and Propp’s “How the Alternating Sign Matrix Conjecture was solved”:   http://www.ams.org/notices/199906/fea-bressoud.pdf Propp’s “The many faces of alternating sign matrices”   http://arxiv.org/pdf/math/0208125v1.pdf Zeilberger’s proof:

# Interesting writing about research in combinatorics

There’s a new article by Richard Stanley in his website called “How the Upper Bound Conjecture Was Proved”. It is a very interesting story, that show how hard and continous work + knowledge of different math areas + attending to

# Interesting writing about research in combinatorics

There’s a new article by Richard Stanley in his website called “How the Upper Bound Conjecture Was Proved”. It is a very interesting story, that show how hard and continous work + knowledge of different math areas + attending to

# Spanning trees of K_{m,n}

Here’s a nice exercise: find the number of spanning trees of the complete bipartite graph . We have given analytic, combinatorial, and algebraic proofs of the fact that there are trees on , you may try to test all methods

# Spanning trees of K_{m,n}

Here’s a nice exercise: find the number of spanning trees of the complete bipartite graph . We have given analytic, combinatorial, and algebraic proofs of the fact that there are trees on , you may try to test all methods

# HW 3 solutions up

I just posted the solutions to HW 3 on the course website, featuring fantastic contributions by David Pardo, Felipe, Alejandro, Brian Cruz, Jorge, Andres Rodriguez, and Matthew. You might be particularly interested in Brian’s significant strengthening of Problem 3.

# HW 3 solutions up

I just posted the solutions to HW 3 on the course website, featuring fantastic contributions by David Pardo, Felipe, Alejandro, Brian Cruz, Jorge, Andres Rodriguez, and Matthew. You might be particularly interested in Brian’s significant strengthening of Problem 3.

# Projects and partners

Are you looking for a project partner? Are you still trying to decide what topic you are going to work on? Feel free to post your thoughts/questions/ideas here.

# Projects and partners

Are you looking for a project partner? Are you still trying to decide what topic you are going to work on? Feel free to post your thoughts/questions/ideas here.

# Parking Functions and Dyck Paths

Federico mentioned in lecture that the number of increasing parking functions of length n is equal to , the nth Catalan number, which suggests that there is a bijection between increasing parking functions of length n and Dyck paths of

# Parking Functions and Dyck Paths

Federico mentioned in lecture that the number of increasing parking functions of length n is equal to , the nth Catalan number, which suggests that there is a bijection between increasing parking functions of length n and Dyck paths of