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# Steven Landsburg

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 Name Steven Landsburg Member for 2 years Seen 3 hours ago Website Location Age
 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. Jun16 comment Maximum likelihood and least squaresWhat's $X$? What's $W$? What's $\beta$? Voting to close as not a real question. Jun16 comment A strange matrix equalityrobninson1: The right hand side is the matrix $tr(B)I$ where $I$ is the identity matrix. Jun16 revised A strange matrix equalitydeleted 133 characters in body Jun16 answered A strange matrix equality Jun14 comment Probability distribution : a number as a randomly built up partitionWhy do you ask? Jun13 comment Game of Chess and axiomatic systemsari: but it's pretty easy to put an upper bound on the number of positions, and even easier to show an upper bound exists. Jun12 comment Prime-Counting FunctionIt's probably off by 1. But why do you ask? Jun12 revised Game of Chess and axiomatic systemsdeleted 9 characters in body Jun12 awarded ● Nice Answer Jun12 answered Game of Chess and axiomatic systems Jun11 comment Random infinite sequence : Can machines generate truly random sequences.This is not a math question. Jun10 comment the graded pieces of the gamma-filtration of Quillen K-theory and Chow groups of a regular schemeNote that I've rewritten the second paragraph of my answer, which originally contained too strong a statement. Jun10 revised the graded pieces of the gamma-filtration of Quillen K-theory and Chow groups of a regular schemeCorrected overly strong statement in second paragraph. Jun10 comment Freeness of a Z[x]-moduleDo you know a spanning set? Jun7 answered Bass' stable range of $\mathbf Z[X]$ Jun7 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". Jun7 comment The cyclic subfactors theory: a quantum arithmetic ?Stefan: I, for one, do not. Jun7 accepted the graded pieces of the gamma-filtration of Quillen K-theory and Chow groups of a regular scheme Jun7 answered Defining a topology in the Power Set Jun7 answered Research topics restricted to students at top universities? Jun6 answered the graded pieces of the gamma-filtration of Quillen K-theory and Chow groups of a regular scheme Jun6 awarded ● Nice Answer Jun6 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.) Jun6 answered Bass' stable range of $\mathbf Z[X]$ Jun6 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. Jun6 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. Jun6 comment Recommended books/lecture notes for vector bundle on algebraic curveWhy not ask the instructor? Jun5 answered Bass' stable range of $\mathbf Z[X]$ Jun4 awarded ● Nice Answer Jun4 comment Iterated calculation of determinantsdarij: 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. Jun4 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. Jun2 awarded ● Popular Question Jun2 comment Boys and Girls RevisitedTim: it is also worth noting that after everyone has reproduced, we do have $E(G/G+B-1)=1/2$. Jun1 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. Jun1 accepted Algebraic K-theory and Homotopy Sheaves May31 answered Algebraic K-theory and Homotopy Sheaves May31 revised How much one can earn on a white noise ? added 28 characters in body May31 answered How much one can earn on a white noise ? May31 awarded ● Necromancer May31 comment Boys and Girls RevisitedI 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. May30 answered What has happened to Lang’s Files and other political texts? May30 comment Boys and Girls RevisitedThanks, Fedja. This is just what I wanted. May30 comment zeros of a homogeneous polynomialMore 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 $F_{13}$, $\lambda=4,10,12$.