Timeline for Random covering of a set
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 18, 2022 at 5:52 | vote | accept | Pluviophile | ||
| Sep 18, 2022 at 5:04 | comment | added | Fedor Petrov | It equals $T/{n\choose k}^n$, where $T=T(n, k)$ is the number of $k$-regular labelled bipartite graphs with $n$ vertices in each part. Equivalently, $T$ is the number of $(0,1)$-matrices of size $n\times n$ and row and column sums $k$. Or, if you prefer, $T$ is a coefficient of $\prod x_i^ky_i^k$ in $\prod_{i, j=1}^n (1+x_iy_j)$. Also, $T$ is a coefficient of $\prod x_i^ky_i^{n-k}$ in $\prod_{i, j=1}^n (x_i+y_j)$. | |
| Sep 18, 2022 at 1:55 | answer | added | Iosif Pinelis | timeline score: 4 | |
| Sep 17, 2022 at 11:04 | comment | added | mathworker21 | what do u want? exact answer? asymptotics? if asymptotics, is, e.g., $k$ fixed and $n \to \infty$? | |
| Sep 17, 2022 at 8:15 | history | asked | Pluviophile | CC BY-SA 4.0 |