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Explicit expression for recursive sums

Claim: The iterated sum $f_k(t_1,\ldots,t_k)$ counts the number of elements the interval $[\emptyset,\lambda]$ of Young's lattice, where $\lambda = (\lambda_1,\lambda_2,\ldots,\lambda_k)$ is the ...
Accepted

Prove positivity of rational functions

Notice that $$F_r(z) = \frac{1}{(1-z)^{r-1}} - \sum_{k=0}^{r-1} \left(\frac{z}{1-z}\right)^k$$ and therefore for $r\geq 4$ and $n\geq 1$, we have \begin{split} [x^n]\ F_r(z) &= \binom{n+r-2}{r-2} -...
• 25.2k

Explicit expression for recursive sums

$f_k(t_1,\dots,t_k)$ is counting the number of integer points in the "Pitman-Stanley polytope" $\Pi_k(t_1,\dots,t_k)$ defined here. The notation $N(\Pi_k(\mathbf{t}))$ is used in this paper, ...
• 43.7k
Accepted

Find all 2-planar drawings of $K_6$ and $K_7$

The list of all good drawings of $K_6$ can be found in the doctoral thesis by Nabil H. Rafla: https://escholarship.mcgill.ca/concern/theses/x346d4920 On pages 164-165 the drawings are described by the ...
• 5,406