S Huntsman
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 Jan 25 comment The lattice of partial partitions @BrianM.Scott- thanks for your comment. I'd been using the order for $\Pi_{\le n}$ (a la Hanlon, Hersh, and Shareshian) instead of $Q_n$ and didn't notice these were different. Jan 25 comment The lattice of partial partitions It didn't occur to me that the partial order they used might be different than the one I had in mind, so obviously this is what I missed. Thanks! Jan 25 accepted The lattice of partial partitions Jan 25 comment The lattice of partial partitions @hardmath - your mapping is why the two lattices clearly have the same size. But when I draw $Q_2$ I get two maximal chains, viz. $() \le (1) \le (1)(2) \le (12)$ and $() \le (2) \le (1)(2) \le (12)$, while for $\Pi_3$ the three maximal chains are $(1)(2)(3) \le (12)(3) \le (123)$, $(1)(2)(3) \le (13)(2) \le (123)$, and $(1)(2)(3) \le (1)(23) \le (123)$. Jan 25 asked The lattice of partial partitions Jun 9 comment Markov chain: join states in Transition Matrix en.wikipedia.org/wiki/Lumpability Jan 4 awarded Autobiographer Dec 15 awarded Caucus Jul 30 comment Why is the volume of a sphere $\frac{4}{3}\pi r^3$? The negative solution to Hilbert's third problem (en.wikipedia.org/wiki/Hilbert%27s_third_problem) strongly suggests (if not shows outright) that this and related questions require calculus in an essential way, and that calculus-free "derivations" are just hiding something. Jul 2 awarded Curious Apr 29 comment Meaning of pullback Consider $f = g \circ \alpha$. The universal property implies that the corresponding pullback satisfies (using Wikipedia notation current at the time of writing) $P = \text{dom } \alpha$, $p_1 = id$, $p_2 = \alpha$, so that $\alpha$ is the pullback of $f = g \circ \alpha$ along $\alpha$. Jan 22 comment How can I explicitly construct a *nice* conformal mapping from a triangle to a square in MATLAB? Jan 22 comment How can I explicitly construct a *nice* conformal mapping from a triangle to a square in MATLAB? @Arkamis--Look at the polygon p1. The stuff you're preoccupied with doesn't have anything to do with the actual polygon, just an easy way to generate points inside it. Jan 22 comment How can I explicitly construct a *nice* conformal mapping from a triangle to a square in MATLAB? I should also note that I've seen mathfaculty.fullerton.edu/mathews/c2003/… and this (or similar maps) doesn't really solve my problem AFAIK. Jan 22 comment How can I explicitly construct a *nice* conformal mapping from a triangle to a square in MATLAB? @Arkamis--I don't think so. That's just the y-limits of the equilateral triangle, which is centered at the origin. Jan 22 asked How can I explicitly construct a *nice* conformal mapping from a triangle to a square in MATLAB? Aug 31 accepted Reference request for Euclidean metric in hyperspherical coordinates Aug 31 asked Reference request for Euclidean metric in hyperspherical coordinates Jul 26 comment Number of item distributions in buckets of different sizes @VladimirDotsenko: I wish I could have read your comment back in 2001! Jul 26 comment Number of item distributions in buckets of different sizes I would hope that this is not closed: if there is a simple answer, I am not aware of it and would like to know it. I previously wondered about this very question many years ago and based on that experience I do not think it should be migrated. For instance, I could not figure out how to make the straightforward appeal to inclusion-exclusion actually work in practice.