Piotr Semenov
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 Dec21 awarded Constituent Dec17 awarded Caucus Feb7 accepted How many ways to distribute $k$ indistinguishable balls over $m$ of $n$ distinguishable bins of finite capacity $l$? Feb7 comment How many ways to distribute $k$ indistinguishable balls over $m$ of $n$ distinguishable bins of finite capacity $l$? sure, I specified the upper limit just to see the finite summation. Thank you for your answer! Feb6 comment How many ways to distribute $k$ indistinguishable balls over $m$ of $n$ distinguishable bins of finite capacity $l$? Just to improve your answer, the upper limit of sum is $\lfloor \frac{k}{l} \rfloor-1$. Feb6 comment How many ways to distribute $k$ indistinguishable balls over $m$ of $n$ distinguishable bins of finite capacity $l$? Just a small typo in your answer. Add $l$ balls to first bin, one have to distribute $k-l$ balls (instead of "$m-l$ units"). Feb6 comment How many ways to distribute $k$ indistinguishable balls over $m$ of $n$ distinguishable bins of finite capacity $l$? Can you kindly explain, why $\binom{k-jl-1}{m-1}$ and not $\binom{k-jl-1}{m-j-1}$? Feb5 asked How many ways to distribute $k$ indistinguishable balls over $m$ of $n$ distinguishable bins of finite capacity $l$? Feb3 comment Number of ways to put $n$ unlabeled balls in $k$ bins with a max of $m$ balls in each bin @Brian What are the sum limits in your formula? The expression from book Enumerative Combinatorics (p. $360$) is $L(n,k,m)=\sum_{j=0}^k (-1)^j C_k^j C_{k+n-j(m+1)-1}^{k-1}$ according to your notation, where $C_k^j$ means the binomial coefficient. Unfortunately, $L(n,k,m)=0$ for any $n \leq k \cdot m$ (Mathematica' showed me that). Somewhere the mistake lives. Can you kindly help me with this problem? Oct29 awarded Scholar Oct29 accepted When is a cyclotomic polynomial over a finite field a minimal polynomial? Oct29 accepted How many irreducible factors does $x^n-1$ have over finite field? Oct22 asked How many irreducible factors does $x^n-1$ have over finite field? Oct21 awarded Student Oct21 comment When is a cyclotomic polynomial over a finite field a minimal polynomial? Thanks! So I did a mistake while suggesting that cyclotomic polynomials are also irreducible in case of finite fields. Oct21 revised When is a cyclotomic polynomial over a finite field a minimal polynomial? deleted 94 characters in body Oct21 comment When is a cyclotomic polynomial over a finite field a minimal polynomial? Please explain it for the following example. Given finite field $\mathrm{F}_q$, I have a decomposition $x^n-1=\prod_{i=0}^{m-1}f_i(x)$ over $\mathrm{F}_q$, where all $f_i(x)$ are cyclotomic. I am not sure that all $f_i(x)$ are minimal polynomials for some elements from extension $[\mathrm{F}_q^r : \mathrm{F}_q]$, where $r$ is a smallest number that $n$ divides $q^r - 1$. What is wrong in that? Oct21 revised When is a cyclotomic polynomial over a finite field a minimal polynomial? added 82 characters in body Oct21 asked When is a cyclotomic polynomial over a finite field a minimal polynomial? Jun27 awarded Critic