2,642 reputation
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bio website www4.ncsu.edu/~plhersh
location Raleigh, NC
age 41
visits member for 2 years, 6 months
seen Nov 25 '12 at 22:16
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.

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Nov
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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 enumerative-combinatorics 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 rank-generating 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 rank-generating function from its unordered list of coefficients?
Nov
14
comment Given the vertices of a convex polytope, How can we construct its Half-Space 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 Half-Space 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 n-ball 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), 406-407. 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.