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Steven Landsburg

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Name Steven Landsburg
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11h
 asked Proper-class sized “ring” with no maximal ideals
13h
 comment Can we efficiently compute a third Nash Equilibrium, given two?
Noah: But in this case, the two equilibria give you no information beyond what can be extracted trivially from knowing the payoffs. (That is, all they give you is the two inequalities $A_{11}>A_{21}$ and $A_{22}>A_{12}$.) So if there were an efficient linear system as you envision, then it would follow that there's such a system using only the payoffs as input. Am I missing something?
14h
 comment Can we efficiently compute a third Nash Equilibrium, given two?
Noah: The question as I understood it wasn't "Is it hard or easy", but "Is it any easier than it was before I knew about the first two equilibria?".
15h
 answered To what equal constant in the Gibbs lemma
22h
 accepted Can we efficiently compute a third Nash Equilibrium, given two?
1d
 answered Can we efficiently compute a third Nash Equilibrium, given two?
1d
 comment Bass' stable range of $\mathbf Z[X]$
Wilberd: Right. I no longer understand why I thought this mattered. Thanks for making this clear.
Jun
16
 comment Maximum likelihood and least squares
What's $X$? What's $W$? What's $\beta$? Voting to close as not a real question.
Jun
16
 comment A strange matrix equality
robninson1: The right hand side is the matrix $tr(B)I$ where $I$ is the identity matrix.
Jun
16
 revised A strange matrix equality
deleted 133 characters in body
Jun
16
 answered A strange matrix equality
Jun
14
 comment Probability distribution : a number as a randomly built up partition
Why do you ask?
Jun
13
 comment Game of Chess and axiomatic systems
ari: but it's pretty easy to put an upper bound on the number of positions, and even easier to show an upper bound exists.
Jun
12
 comment Prime-Counting Function
It's probably off by 1. But why do you ask?
Jun
12
 revised Game of Chess and axiomatic systems
deleted 9 characters in body
Jun
12
 awarded ● Nice Answer
Jun
12
 answered Game of Chess and axiomatic systems
Jun
11
 comment Random infinite sequence : Can machines generate truly random sequences.
This is not a math question.
Jun
10
 comment the graded pieces of the gamma-filtration of Quillen K-theory and Chow groups of a regular scheme
Note that I've rewritten the second paragraph of my answer, which originally contained too strong a statement.
Jun
10
 revised the graded pieces of the gamma-filtration of Quillen K-theory and Chow groups of a regular scheme
Corrected overly strong statement in second paragraph.
Jun
10
 comment Freeness of a Z[x]-module
Do you know a spanning set?
Jun
7
 answered Bass' stable range of $\mathbf Z[X]$
Jun
7
 comment Bass' stable range of $\mathbf Z[X]$
I'm confused too, but here's my best approximate guess of what he means: First, let $A$ be a ring constructed per V's suggestion. It suffices to show that $sr(A)\ge 3$. For this, it suffices to show that $SL_3(A)\neq E_3(A)$, and for this it suffices to show that $SK_1(A)\neq 0$. And indeed, examples of such $A$ are known for which $SK_1\neq 0$. So, modulo filling in details, this works if Vaserstein's "2" was a typo for "3".
Jun
7
 comment The cyclic subfactors theory: a quantum arithmetic ?
Stefan: I, for one, do not.
Jun
7
 accepted the graded pieces of the gamma-filtration of Quillen K-theory and Chow groups of a regular scheme
Jun
7
 answered Defining a topology in the Power Set
Jun
7
 answered Research topics restricted to students at top universities?
Jun
6
 answered the graded pieces of the gamma-filtration of Quillen K-theory and Chow groups of a regular scheme
Jun
6
 awarded ● Nice Answer
Jun
6
 comment Bass' stable range of $\mathbf Z[X]$
Jeremy: I'm wondering that too. Presumably one can work backward from this argument to construct the row explicitly, but I'm trying to resist the temptation to start a calculation that threatens to kill my afternoon. (On another front, I quoted Vaserstein when I said "small ideal", but I presume this must mean "principal ideal" to make the argument work.)
Jun
6
 answered Bass' stable range of $\mathbf Z[X]$
Jun
6
 comment Bass' stable range of $\mathbf Z[X]$
I've written to both Suslin and Vaserstein about this and will report back if I learn anything.
Jun
6
 comment Bass' stable range of $\mathbf Z[X]$
This is right. For a finitely generated ring of dimension at least 3, we always have stable range $\le$ the dimension of the ring.
Jun
6
 comment Recommended books/lecture notes for vector bundle on algebraic curve
Why not ask the instructor?
Jun
5
 answered Bass' stable range of $\mathbf Z[X]$
Jun
4
 awarded ● Nice Answer
Jun
4
 comment Iterated calculation of determinants
darij: At the very least, you are right that this needs more argument. I will try to find time to try to think about how to try to supply that argument.
Jun
4
 comment Must $|Grp(G,H)|$ divide $|Grp(K,H)|$ for certain groups $G,H,K$
Let $K=S_3$, $G={\mathbb Z}/2{\mathbb Z}$, $H=S_3$. There are four maps from ${\mathbb Z}/2{\mathbb Z}$ to $S_3$. There are ten maps from $S_3$ to itself (the compositions of the above four with the projection onto ${\mathbb Z}/2{\mathbb Z}$ and the six inner automorphisms). Four does not divide ten, so the answer to your question is no.
Jun
2
 awarded ● Popular Question
Jun
2
 comment Boys and Girls Revisited
Tim: it is also worth noting that after everyone has reproduced, we do have $E(G/G+B-1)=1/2$.
Jun
1
 comment How much one can earn on a white noise ?
Joel: There are two reasons to be skeptical of the "trend plus noise" model, neither of them strictly mathematical. First, it's almost impossible to incorporate this model into an equilibrium model in which profit-maximizing traders respond to a price process and thereby change that process. (More prosaically, this model allows for unexploited profit opportunities, whereas we ordinarily assume that unexploited profit opportuntities lead to trading behavior that causes those opportunitites to vanish.) The second reason is the empirical evidence from real world financial assets.
Jun
1
 accepted Algebraic K-theory and Homotopy Sheaves
May
31
 answered Algebraic K-theory and Homotopy Sheaves
May
31
 revised How much one can earn on a white noise ?
added 28 characters in body
May
31
 answered How much one can earn on a white noise ?
May
31
 awarded ● Necromancer
May
31
 comment Boys and Girls Revisited
I too failed at first to grasp Fedja's wonderful idea, but for me it all came clear when I read his response to Emil's comment. Thanks for elaborating it.
May
30
 answered What has happened to Lang’s Files and other political texts?
May
30
 comment Boys and Girls Revisited
Thanks, Fedja. This is just what I wanted.
May
30
 comment zeros of a homogeneous polynomial
More data: Here are all allowable $\lambda$ for small fields. For $F_3$, $\lambda=2$. For $F_5$, $\lambda=1,2$. For $F_7$, $\lambda=1,2,4$. For $F_{11}$, $\lambda=4,5,7,8$. For $F_{13}$, $\lambda=4,10,12$.