# To end the semester . . .

I just wanted to share this picture. (I took this picture earlier last week at Rosamunde in San Francisco.) Happy end of semester to everyone. Cheers!

# To end the semester . . .

I just wanted to share this picture. (I took this picture earlier last week at Rosamunde in San Francisco.) Happy end of semester to everyone. Cheers!

# Class Notes

Hello everyone, I TeX’d up a bunch of notes from the lectures and lecture notes and thought others might be interested in getting a copy of them. Use with caution – these notes are not complete and there may be

# Class Notes

Hello everyone, I TeX’d up a bunch of notes from the lectures and lecture notes and thought others might be interested in getting a copy of them. Use with caution – these notes are not complete and there may be

# Hopfication sensation across the nation

We have said that non-finite dimensional Hopf algebras may not have a linear dual, but that if they are graded we can fake it with a graded dual. For the non-graded case, how much information is lost if we define

# Hopfication sensation across the nation

We have said that non-finite dimensional Hopf algebras may not have a linear dual, but that if they are graded we can fake it with a graded dual. For the non-graded case, how much information is lost if we define

# group of characters

In our lecture notes, it says that the group of characters of a hopf algebra is the set of algebra maps from H to k.The operation of this group is the convolution product which is related to the algebra’s coproduct. Do the

# group of characters

In our lecture notes, it says that the group of characters of a hopf algebra is the set of algebra maps from H to k.The operation of this group is the convolution product which is related to the algebra’s coproduct. Do the

# Two important comments on the scalar product

1. Again, please note the mistake I made in class and on the lecture notes. I am about to correct the notes and reupload them: https://hopfcombinatorics.wordpress.com/2012/04/26/latex-se_lambda-1n-h_lambda-and-a-mistake-in-lecture-3/ 2. The inner product on Sym has the very nice property that it is

# Two important comments on the scalar product

1. Again, please note the mistake I made in class and on the lecture notes. I am about to correct the notes and reupload them: https://hopfcombinatorics.wordpress.com/2012/04/26/latex-se_lambda-1n-h_lambda-and-a-mistake-in-lecture-3/ 2. The inner product on Sym has the very nice property that it is

# S(e_n) = (-1)^n h_n, and a mistake in lecture

1. In class I explained that for any partition of , and that this follows from the equation for . Can someone provide a proof of this? (Hint: there are elegant formulas for the generating functions and .) 2. I made

# S(e_n) = (-1)^n h_n, and a mistake in lecture

1. In class I explained that for any partition of , and that this follows from the equation for . Can someone provide a proof of this? (Hint: there are elegant formulas for the generating functions and .) 2. I made

# Dominance order

Today in class I claimed that the transition matrix from the elementary symmetric functions to the monomial symmetric functions is upper triangular. However, it is not trivial to decide what order the rows and columns of this matrix should be

# Dominance order

Today in class I claimed that the transition matrix from the elementary symmetric functions to the monomial symmetric functions is upper triangular. However, it is not trivial to decide what order the rows and columns of this matrix should be