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 Feb28 comment Element-Wise Proofs? The crucial step, from 2nd to 3rd statement, is not obvious (at this level). How do you justify the manipulation of English 'and's and 'or's? Feb28 revised How to detect antitransitivity from an adjacency matrix? added new explanation Feb28 comment How to detect antitransitivity from an adjacency matrix? I'm going to be a bit intrusive and say that you really shouldn't want a 'measure' of how transitive a graph is. A graph is either transitive or it is not (all it takes is one edge to prevent it). There might be a fractional version of this 0-1 property (sort of like fractional chromaticity) but I'm not fluent enough with that to come up with a meaningful fractional-transitive property. Instead I think you want to get rid of cycles (in a directed graph). Then you can take a transitive closure to get the 'is-a' poset. I'm editing my answer to reflect this. Feb27 comment Factorial and exponential dual identities Excellent...it took me a while to appreciate. Sometimes even the simplest manipulation can be inscrutable, like the integral equal to $\frac{1}{1-t}$. What this all does for me though is convince me in the simplest way possible that the second identity is just the best analytic continuation of the factorial function (just the simplest way that is). Feb27 accepted Factorial and exponential dual identities Feb27 comment Factorial and exponential dual identities Excellent! Thanks. How did you come to know that? As usual the algebra is almost trivial after the fact. Any hints as to the meaning import (like Qioachu's question in his 2nd link)? Feb23 comment The ratio in terms of sets Can you clarify your question? Your first question asks about A/B, which is then $\frac{(2n-1)!!}{4^n}$, and you second asks about A which you seem to have answered already. Feb23 answered How to detect antitransitivity from an adjacency matrix? Feb23 comment The Hexagonal Property of Pascal's Triangle @milcak: can you give an example of a proof of an identity involving just binomial coefficients that would be sufficient to be called 'combinatorial' by you? You may want to explain to what degree your example is 'pure' or avoids the use of 'how pascal's triangle is constructed'. (before dismissing my example, you should confirm that it does not use Pascal's identity) Feb16 answered Algorithm complexity in for loop Feb16 answered Has there been a rigorous analysis of Strassen's algorithm? Feb16 comment Has there been a rigorous analysis of Strassen's algorithm? The 'rigorous' analysis won't depend on the specific implementation language. There are too many vagaries in computer languages, and anyway they end up not contributing much one way or the other to the analysis. Most references for such algorithm analysis will just look at the recurrence and try to extract constants and lower order terms from the Master Method. Feb14 revised Are negative or noninteger powers still power series? added 3 characters in body Feb14 answered Are negative or noninteger powers still power series? Feb13 comment Why is Euler's Identity stated the way it is? @Yuval: "...there's not much merit..."? Really? Feb12 comment Calculate distance between two points N,W,E,S Manahattan refers to the idea that in Manhattan which has mostly just east/west and north/south streets in a perfect grid, you can only follow rectilinear streets to get from any point to any other (you can't cut corners or go in diagonals). Feb12 revised How can I systematically find a solution to this problem? added 1 characters in body Feb12 comment Solving a set of recurrence relations From that last relation for $F_n$ you can 'solve' for $E$ (in terms of $F$ and $C$, then substitute into the first relation. Then you'll have a relation on just $F$ and $C$. Since you already have a complete non-recursive solution for $C$, you'll be able to solve for $F$. Feb12 comment Calculate distance between two points N,W,E,S I think for your distances that 'wrap around' you want to add 1 to each. What's the distance between two squares that are adjacent? 1, right? then if there's a square between thew two, the distance should be 2. You're counting the steps going from the center of one square to another, not from the nearest edges of the two. Feb12 comment Calculate distance between two points N,W,E,S @FeRtoll: I see what you're doing with your examples, but it seems a little 'mixed' to me. That is, if the two points appear closer without having to go over the edges, you seem to want to use the Euclidean distance (the Pythagorean formula). But if it seems closer over the edge, you take the Manahattan distance. To get this, in my definition for $d_t$, you'd change $d(p_1,p_2)$ to be the Euclidean distance instead of Manhattan, and keep the rest Manhattan. I don't think you really -want- to do this, I'm just saying that that's how you would do it if you really wanted to.