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 Apr 18 awarded Notable Question Sep 24 awarded Autobiographer Jul 29 awarded Popular Question Jul 2 awarded Curious Feb 26 awarded Popular Question Nov 4 awarded Popular Question Aug 6 awarded Notable Question Jun 25 awarded Promoter Apr 27 awarded Popular Question Mar 26 answered A question about the size of a L1 ball Mar 24 comment A question about the size of a L1 ball Thank you so much for your reply. For question (1), could you please explain in more detail why $\sum\limits_{b=0}^{\sqrt{n}}b^{|\mathcal{X}|-1}$ is approximately equal to $\sqrt{n}\cdot\sqrt{n}^{|\mathcal{X}|-1}$? Mar 24 comment A question about the size of a L1 ball The third question is here: (3)For the new answer, since the number of balls in any entry of the matrix, including those in the last column, should not be negative, we can not pick any number freely from $[-\sqrt{n},\sqrt{n}]$. So the number of actual pmfs in $\mathcal{T}_{s^*}$ is less than $\sqrt{n}^{(|\mathcal{Y}|-1)\cdot|\mathcal{X}|}$. Therefore, under this constraint, how to understand the new answer? Mar 24 comment A question about the size of a L1 ball Thank you very much for your answer. But I have three questions as follows: (1) in your old answer, when putting at most $\kappa\sqrt{n}$ balls to $|\mathcal{X}|$ bins and summing for the number of balls from 0 to $\sqrt{n}$ if omitting $\kappa$, I think the total possibilities should be $\sum\limits_{b=0}^{\sqrt{n}}b^{|\mathcal{X}|-1}$. Why you say it is $\sqrt{n}\cdot\sqrt{n}^{|\mathcal{X}|-1}$? (2)Why does "in most cases this distribution will be quite even" so that the number of balls for each row can be obtained by dividing the total balls $\kappa\sqrt{n}$ by $|\mathcal{X}|$? Mar 3 comment A question about the size of a L1 ball $\mathcal{X}$ is the alphabet of symbols for $X$. $\mathcal{X}^n$ is all the sequence of length $n$ drawn from $\mathcal{X}$. Mar 3 asked A question about the size of a L1 ball Jan 27 accepted equivalence of 1-norm and relative entropy? Jan 27 comment equivalence of 1-norm and relative entropy? Yes, you are right. I should have considered the circumstances that $q_i=0$ for some symbol. But what if I put a restriction on $q$ that all $q_i$'s are positive? Jan 27 answered equivalence of 1-norm and relative entropy? Jan 27 revised equivalence of 1-norm and relative entropy? added 7 characters in body Jan 27 asked equivalence of 1-norm and relative entropy?