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