Kevin O'Bryant

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 Name Kevin O'Bryant Member for 3 years Seen yesterday Website Location New York City Age 42
Research: additive number theory; combinatorial number theory. Faculty at City University of New York, at the Staten Island and Graduate Center campuses.
 May14 revised two boy scouts problemsadded link to wikipedia Apr8 awarded ● Nice Answer Mar20 awarded ● Nice Answer Mar12 comment From reducible polynomial to an irreducible oneThis is a ring (just not one with unity). In any case, the OP asked for "an algebraic construction". Mar7 answered From reducible polynomial to an irreducible one Feb19 comment Most inconsistent rankingCall the matrix $M=(m_{ij})$. Then, if I understand correctly, total sum of the variance of each row'' is defined to be $\sum_{i=1}^k \frac1n \sum_{j=1}^n (m_{ij}-\frac 1n \sum_{\ell=1}^n m_{i\ell})^2$. Feb19 revised Most inconsistent rankingchanged sd to variance Feb19 revised Most inconsistent rankingadded $k=3$ Feb19 answered Most inconsistent ranking Feb12 awarded ● Nice Answer Jan7 awarded ● Good Answer Jan7 comment Have discovered a recursive formula for Prime Density - is this known?If you change "proof" to "argument", and change the question to "are there infinitely many $n$ where this underestimates the true density", and you'll avoid a closed question. Jan7 comment Have discovered a recursive formula for Prime Density - is this known?I get $D_3 = 4/15$ by your formula, but the actual density should be $6/23$. Through small values of $n$, I find that the actual density is about $0.01$ below your formula, but this is the sort of thing that small $n$ are misleading about. Jan5 comment Is pi a good random number generator?@Victor: Isn't that what "predictability" means? Dec28 revised Status of the 196 conjecture?Changed "Lycrel" to "Lychrel" Dec28 revised Status of the 196 conjecture?addressed a comment about the connection between f and s and palindromes Dec28 comment Status of the 196 conjecture?Typically, this sort of heuristic argument cannot be "fixed" because the underlying process is not random, but it can be improved. Aaron's answer explains some of the dependence, and one could try to bring that into this probabilistic model. One could then try and push the model to give the probability of, say, a 20 digit number having one of its first 50 iterates a palindrome. Such a probability can be compared to experiment as a way of assessing the heuristic. But to be clear: there is no chance that this will lead to a proof. Dec26 answered Status of the 196 conjecture? Dec23 revised The origin of sets?added 191 characters in body Dec22 answered The origin of sets? Dec20 comment unique sums in a finite direct product of sets of integersA more natural way to state the condition is that $|A_1+\cdots+A_h| = |A_1| \cdots |A_h|$ (the parameter $h$ is more common than $n$ here). These come up in additive combinatorics, but I don't know a name for them. If $A_1= \dots =A_h$, and you don't care about the ordering of the sum (i.e., one can reorder the $b_i$ so that $a_i=b_i$), these are called "Sidon Sets", also $B_h$-sets. Dec19 awarded ● Nice Answer Dec19 answered Publishing a bad paper? Dec4 awarded ● Good Answer