Harry Altman at the University of Michigan
My name is Harry Altman. I
recently graduated from the
University of Chicago, and am currently studying mathematics at the University
of Michigan. I mostly know algebra and combinatorics, but recently I've done
some work on integer complexity with Joshua Zelinsky. Jeffrey Lagarias is my
Most recent updates:
2013 October 11 -- Integer Complexity
and Well-Ordering is now on arXiv!
2013 May 8 -- Added various images.
2012 November 10 -- Added print version of Numbers With Integer Complexity Close
to the Lower Bound.
2012 October 16 -- Numbers With Integer
Complexity Close to the Lower Bound is now published!
2012 June 1 -- Updated Spelling Elements with
Elements to account for Flerovium (Fl) and Livermorium (Lv).
2012 May 29 -- Added The Co-Files. Changed order of
I can be reached via email at . (If you can't see my email address, that's because it's been
URL.) My PGP public key can be found here.
Papers and drafts
Polished drafts, should be readable
Nothing to go here at the moment.
Old drafts, may be incomprehensible and out of date
Numbers with integer complexity close to the
lower bound I (with Joshua Zelinsky): In which we devise a method for
classifying numbers whose integer
complexity is close to the lower bound, and derive various
consequences. This is somewhat out of date and not very readable; I am
currently working on fixing that.
- Classification of n with
d(n)≤22d(2): The table of results from the computation described in
the above draft. Currently not included in the draft proper, as even in this
compressed form it's 7 pages long. We have since come up with a way of doing
these computations algorithmically, so this is no longer fully necessary. Also
I may not have corrected the few mistakes in it.
- Numbers with integer complexity close to the
lower bound: A rather longer version of the above paper in which we
discuss some things we didn't have room for in the short version. Currently in
the process of being turned into multiple papers which will actually be
readable. Some of the conjectures in here have since been proved.
Highest few sums and products of ones: A
write-up of an idea I don't intend to publish - the method doesn't generalize;
my newer results with Joshua Zelinsky in the above draft extend and obsolete it
(hence all the references to the improvements made in our forthcoming paper).
Still I think the method is interesting and was worth writing up.
- Here is the Haskell code used for the computations.
Informal bloggy writing on problems I don't necessarily know much of anything about.
Here are miscellaneous files I wish to put in public view:
Here are some drawings that people have given me which I have bothered to scan:
And here are some assorted other images.