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 Apr 2 comment Is there a connection between the “independent sets” in matroids and “independent sets” in graph theory? The independent sets of matroids generalize sets of linearly independent vectors in a vector space. Mar 10 comment How do you calculate a probability of at least one success with fractional attempts? Hmm.. I sort of understand but I don't think this is enough explanation to answer sufficiently. In order to make progress, I think it is required to explicitly relate successes to (fractional) attempts. Otherwise, we have no way to understand how to apply the odds of success. Mar 10 comment How do you calculate a probability of at least one success with fractional attempts? This will likely depend on the exact meaning of a "fractional attempt". What does it mean to roll 0.5 times? Can you get half a success on half a roll? Feb 17 comment Complexity Of Recognising Complete Multipartite Graphs Graphclasses shows that complete multipartite graphs are recognizable in polynomial time via a finite forbidden subgraph characterization (since complete multipartite graphs are $\overline{P_3}$-free). This doesn't answer your question about linear time recognition, though. Jan 25 comment A rather special monoid @Lehs Is the obvious way to compose subsets as follows: Given $S, T \subseteq \mathcal{P}(S_n)$, $ST = \{u | \exists s\in S, t\in T, st = u\}$? So, if $S = \{x\}$ and $T = \{x^{-1}\}$, does $ST = \{e\}$? Nov 17 comment Zero-One Optimization I am aware of some heuristic approaches to the basic PARTITION problem but those may or may not be applicable to your situation. For example, if $n$ (the number of $A_i$) is large, then I suspect that your problem's characteristics diverge significantly from PARTITION. The effectiveness of heuristic approaches may be dependent on the precise parameters of your problem instances (e.g.: the number of $A_i$, the range of $c$, etc...). Nov 17 answered Zero-One Optimization Oct 20 comment How many ways are there to pile $n$ “$1\times 2$ rectangles” under some conditions? I found the connection to "directed animals" by checking OEIS for each of the columns in the first table. Oct 20 awarded Yearling Oct 20 revised How many ways are there to pile $n$ “$1\times 2$ rectangles” under some conditions? Added statement of corollary; minor wording change Oct 19 revised How many ways are there to pile $n$ “$1\times 2$ rectangles” under some conditions? Fixed definition of "directed animal" Oct 19 answered How many ways are there to pile $n$ “$1\times 2$ rectangles” under some conditions? Aug 5 answered Vertex Reconstruction Conjecture For Asymmetric Graphs Jul 24 awarded Organizer Jul 24 revised Prove it by theory of combination removed algebraic-geometry tag Jul 24 suggested approved edit on Prove it by theory of combination Jun 4 comment The $5n+1$ Problem It's not clear from the excerpt I quoted, but in that article the "size" of a cycle refers to the number of distinct odd elements in the cycle, not the length. Apr 22 answered On the invertibility of adjacency matrix Feb 25 awarded Yearling Feb 25 answered Hash functions for unordered data