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Results tagged with co.combinatorics
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user 10668
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
6
votes
1
answer
527
views
Can information be extracted more precisely using more random trials?
Write $n$ iid draws of $(x,y)$ as $(x^n, y^n)$. Fix $R\in (0,H(x))$. What is the min of $n^{-1}H(y^n|f(x^n))$ over maps $f$ with range $\lbrace 1,\dots,\exp nR\}$, taking $n\to \infty$?
2
votes
1
answer
199
views
Do enough permutations of an initial set probably cover most permutations?
Fix $\alpha, \epsilon \in(0,1)$. Take $(S_n)_n$ to be any sequence of sets with each $S_n$ containing $ \lceil (n!)^\alpha\rceil$ permutations of $n$ elements. Also build another sequence of sets $(S_ …
0
votes
Transforming random variables for having good property?
No, of course not.
You cannot generally get $X,Y$ to surely satisfy your desired typical events $\Omega$ and $\Lambda$ by transforming them individually. Let alone finding a somehow negligibly-distor …
0
votes
Accepted
Do enough permutations of an initial set probably cover most permutations?
If $M_n$ is all permutations of $n$ elements then $\{\pi \circ S_n: \pi \in M_n\}$ is precisely a $|S_n|$-fold cover of $M_n$. Choosing $S_n^\ast$ and then forming the composition of $S_n^\ast$ with $ …