bio  website  www4.ncsu.edu/~plhersh 

location  Raleigh, NC  
age  40  
visits  member for  1 year, 11 months 
seen  Nov 25 '12 at 22:16  
stats  profile views  3,760 
My research is in algebraic combinatorics, especially topological aspects of combinatorics.
My plan here at MO seems to be (roughly) to answer some combinatorics questions and to ask some topology questions.
I'm an associate professor at North Carolina State University.
1d

awarded  Nice Answer 
Jun 25 
awarded  Excavator 
May 28 
awarded  Good Answer 
May 4 
awarded  Yearling 
Dec 1 
awarded  Necromancer 
Nov 25 
revised 
Salié permutations and fair permutations
edited tags 
Nov 20 
comment 
Combinatorial Morse functions and random permutations
Hi Bruce, welcome to MathOverflow! You might consider registering your account (if you might participate more  I've been finding this a great place to learn interesting math). 
Nov 19 
comment 
Combinatorial Morse functions and random permutations
@Liviu: I like your question and have been meaning to think about it for some time now, but never seem to have the time. Meanwhile, I hope you don't mind that I added an enumerativecombinatorics tag to it, in case that might draw some additional other people's attention to your question. It seemed to me at least like an interesting relaxation of counting alternating permutations. 
Nov 19 
revised 
Combinatorial Morse functions and random permutations
edited tags 
Nov 17 
comment 
Quotations about the power of simple ideas
Jonah: in case you are interested, the motto of the Ross program is "Think deeply of simple things." 
Nov 16 
comment 
When can we determine an $f$vector or rankgenerating function from its unordered list of coefficients?
Richard, Thank you for your thoughts on this. I was also wondering about complexes with convex ear decompositions, but will need to spend some time with this. By the way, one reason I was quite interested in the question I linked to above is that I've been trying to figure out how to do some things in a way that'd be sensitive to field characteristic, and it seemed like an answer to that question might help. 
Nov 15 
asked  When can we determine an $f$vector or rankgenerating function from its unordered list of coefficients? 
Nov 14 
comment 
Given the vertices of a convex polytope, How can we construct its HalfSpace representation
Ziegler has more than one book, but I'm sure Dan means the one "Lectures on polytopes", which does discuss going back and forth between $V$representation and $H$representation (i.e. vertex representation and hyperplane representation) of a polytope. 
Nov 14 
comment 
Given the vertices of a convex polytope, How can we construct its HalfSpace representation
Are the columns of $A$ supposed to be the vectors in $V$? What is $m$? Thank you for clarifying. 
Nov 14 
comment 
What is the homotopy type of the space of the homeomorphisms of the nball such that the homeomorphism restricted to the boundary is isotopic to the identity?
I'm not sure about this, but perhaps the original reference for Alexander's trick might be: J.W. Alexander, On the deformation of an $n$cell, Proc. Nat. Acad. Sci. USA 9 (1923), 406407. At least this is the reference given by Kirby and Siebenmann for "Alexander's isotopy" on p. 17 in "Foundational essays on topological manifolds, smoothings, and triangulations" (which is a compilation of key papers written by one or both of them). There is no MathSciNet review of this paper from 1923 to check, obviously. 
Nov 12 
comment 
Meaning of a quote of Doubilet,Rota and Stanley on harmonic analysis and combinatorics
If you are interested in connections between combinatorics and harmonic analysis in general, whether or not they have to do with generating functions, you could try googling "Kakeya set" or "arithmetic combinatorics" as a couple of starting points. 
Nov 12 
answered  Meaning of a quote of Doubilet,Rota and Stanley on harmonic analysis and combinatorics 
Nov 11 
comment 
A weaker concept of graph homomorphism
I would guess that one reason for the emphasis on the existing definition is that it is convenient for graph coloring problems, since a coloring of $G$ with $r$ colors is a graph homomorphism from $G$ to $K_r$. But I've only been watching this area from afar, e.g. the development of topological lower bounds on chromatic numbers. 
Nov 10 
comment 
Is the following construction of the 0Hecke monoid (well) known?
Following up on Alexander's comment, you might also find it interesting to take a look at work of A. Knutson and E. Miller on subword complexes where they study properties of the `Demazure product', which is exactly the 0Hecke product. It also appears in work of Drew Armstrong on sorting orders and in work of mine on total positivity. I had given an answer along these lines, but decided it wasn't really an answer to your question to your question. 
Nov 10 
comment 
Meaning of a quote of Doubilet,Rota and Stanley on harmonic analysis and combinatorics
In addition to the theory of species being a good source for your question 1, so is chapter 5 of Enumerative Combinatorics, Volume 2, by Richard Stanley. 