# Takeuchi’s Formula Vs. the Hopf Algebra diagram

I believe I was able to compute the antipode of G with help from a very patient classmate using the Hopf Algebra diagram. But in Federico’s office hours he suggested that it would be easier to use Takeuchi’s formula. I

# Takeuchi’s Formula Vs. the Hopf Algebra diagram

I believe I was able to compute the antipode of G with help from a very patient classmate using the Hopf Algebra diagram. But in Federico’s office hours he suggested that it would be easier to use Takeuchi’s formula. I

# Resources for flat graph algebras

Hey everyone. I found the following papers and lecture that pertain to flat graph algebras. Hope you find them as useful as I did. Dejan Delić “Finite Bases for Flat Graph Algebras” Journal of Algebra 2002 William A Lampe “Full

# Resources for flat graph algebras

Hey everyone. I found the following papers and lecture that pertain to flat graph algebras. Hope you find them as useful as I did. Dejan Delić “Finite Bases for Flat Graph Algebras” Journal of Algebra 2002 William A Lampe “Full

# Short HW 1

Problem 1 part d Silly question: What is the formula of the antipode for simple graphs and should we use Schmitts or this new formula suggested in this paper http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&ved=0CC8QFjAB&url=http%3A%2F%2Fwww.dmtcs.org%2Fdmtcs-ojs%2Findex.php%2Fproceedings%2Farticle%2Fdownload%2FdmAO0146%2F3596&ei=kBWOT5HpPKaYiQKN6PGDDw&usg=AFQjCNFZhp2LR4Yo8iRDu4lB3ugtjuIKkA? Thank you! 🙂

# Short HW 1

Problem 1 part d Silly question: What is the formula of the antipode for simple graphs and should we use Schmitts or this new formula suggested in this paper http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&ved=0CC8QFjAB&url=http%3A%2F%2Fwww.dmtcs.org%2Fdmtcs-ojs%2Findex.php%2Fproceedings%2Farticle%2Fdownload%2FdmAO0146%2F3596&ei=kBWOT5HpPKaYiQKN6PGDDw&usg=AFQjCNFZhp2LR4Yo8iRDu4lB3ugtjuIKkA? Thank you! 🙂

# Dempster-Shafer Belief function

This last week, my bioinformatics class was introduced to this Bayesian function (see http://www.blutner.de/uncert/DSTh.pdf for more). What got me wondering was this measure: Given an event frame A, you can measure the probabilities not just of each individual event, but each

# Dempster-Shafer Belief function

This last week, my bioinformatics class was introduced to this Bayesian function (see http://www.blutner.de/uncert/DSTh.pdf for more). What got me wondering was this measure: Given an event frame A, you can measure the probabilities not just of each individual event, but each

# definition of flats

are flats always connected edges (it looks that way but I don’t see it as part of the definition) are loops edges? flats?(1,1)

# definition of flats

are flats always connected edges (it looks that way but I don’t see it as part of the definition) are loops edges? flats?(1,1)

# Lecture 22: More on counting faces of polytopes

Some comments on the f-vectors of polytopes. 1. (Upper bound theorem.) Given a dimension d and a number of vertices n, what is the greatest number of k-faces (or the greatest ) that a polytope can have? The “cyclic polytope”

# Lecture 22: More on counting faces of polytopes

Some comments on the f-vectors of polytopes. 1. (Upper bound theorem.) Given a dimension d and a number of vertices n, what is the greatest number of k-faces (or the greatest ) that a polytope can have? The “cyclic polytope”

# Lecture 22: Mystery polytope

As we discussed in class today: Can you find a polytope whose h-vector is the n-th row of Pascal’s triangle?

# Lecture 22: Mystery polytope

As we discussed in class today: Can you find a polytope whose h-vector is the n-th row of Pascal’s triangle?