4,160 reputation
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bio website jamespropp.org
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visits member for 4 years, 11 months
seen 2 hours ago

I am interested in combinatorics, probability, dynamical systems, and various other topics.


2h
revised Notions of positivity for q-polynomials
added 5 characters in body
18h
revised Notions of positivity for q-polynomials
Clarified that coefficients need not be positive
18h
asked Notions of positivity for q-polynomials
Dec
20
revised Nonperiodic points of piecewise-linear homeomorphisms
added 212 characters in body
Dec
20
accepted Nonperiodic points of homeomorphisms of a ball
Dec
20
comment Nonperiodic points of homeomorphisms of a ball
The original journal reference for this theorem is D. Montgomery. Pointwise periodic homeomorphisms, Amer. J. Math. 59 (1937), 118-120. Thanks!
Dec
19
comment Nonperiodic points of homeomorphisms of a ball
What is the "doubling" trick Rivin is referring to?
Dec
19
awarded  Nice Question
Dec
19
revised Nonperiodic points of piecewise-linear homeomorphisms
added 188 characters in body
Dec
19
asked Nonperiodic points of homeomorphisms of a ball
Dec
18
comment Nonperiodic points of piecewise-linear homeomorphisms
The paragraph "The sets $E_{n⋅k}∩$ △′ are closed. They might have nonempty interiors but the complement contains a controlable open set near the boundary of $E_n$. It is sufficient to apply the proof Baire theorem and conclude that $E_{n⋅k}$ do not cover △′. The later leads to a contradiction" is unclear to me.
Dec
17
comment Nonperiodic points of piecewise-linear homeomorphisms
I still don't understand. I'm going to post a bounty, so that Anton (or others) will have an extra incentive to write a clear and complete proof.
Dec
15
comment Nonperiodic points of piecewise-linear homeomorphisms
In the article-in-progress arxiv.org/abs/1310.5294, David Einstein and I prove that a certain piecewise-linear homeomorphism on the order polytope of the poset $[2] \times [2]$ has infinite order, by constructing arbtrarily long orbit-segments. (Actually, we don't do this in the current draft, but we plan to add details soon.) We'd like to know that nonperiodic points exist, and indeed that "most" point are nonperiodic, in the sense of measure or the sense of category. And of course we'd like to know this for other, similar examples.
Dec
15
comment Nonperiodic points of piecewise-linear homeomorphisms
Anton, your comment about rectangles was very helpful, and I'll explain in a minute why I need this result, but first let me ask why we can conclude that the sets $E_{n \cdot k}$ do not cover $\Delta'$. I don't follow this step.
Dec
13
comment Nonperiodic points of piecewise-linear homeomorphisms
I don't understand the sentence "They might have nonempty interiors but the complement contains a controlable open set near the boundary of $E_n$" (partly because I don't know what "controlable" means).
Dec
11
asked Nonperiodic points of piecewise-linear homeomorphisms
Dec
2
accepted A generalized mean-value theorem
Dec
2
asked A generalized mean-value theorem
Nov
14
accepted Origin of the numbers game
Nov
14
comment Origin of the numbers game
I hear that Knuth studied it as well; can anyone provide a pointer to Knuth's article?