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Results tagged with co.combinatorics
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user 119995
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
15
votes
Minimum number of $|\cdot|$ operations necessary to express $\max$
This is just a tighter analysis of the analysis from @GH from MO.
Let $f(n)$ be the minimum number of $|\cdot|$ operations to compute $\max(x_1, \ldots, x_n)$. Then $f(1)=0$ and for $n\geq 1$:
$$f(n)\ …
- 662
4
votes
2
answers
265
views
Intuition on inequality in proving a bound on the sum of squares of degrees of a graph
Given a simple connected graph $G$ with $n$ vertices and $m$ edges, let $d_1, ..., d_n$ denote the degrees of the vertices of the graph. In this very short paper, the author prove the inequality
$$\su …
- 662
25
votes
1
answer
1k
views
Expected height of a poset?
I am interested in any known results/empirical studies done on the average height of a poset with $N$ elements. Obviously this would depend on how that poset relation was randomly defined, however, at …
- 662
1
vote
0
answers
117
views
Upper bound $\sum_{i=1}^m \sum_{j=1}^n p_{i,j}(1-p_{i,j})$
Let
$$p_{i,j} = \frac{\sum_{l=i}^{i+j-1} {l-1 \choose i-1} {m+n-l \choose m-i}}{{m+n \choose n}}$$
I am interested in approximating/upper bounding the sum
$$ \sum_{i=1}^m \sum_{j=1}^n p_{i,j}(1-p_{i,j …
- 662