All Questions
Tagged with applied-mathematics co.combinatorics
10 questions
2
votes
0
answers
209
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Literature on Lyndon words and the Lie commutator
Since I lost my paper notes in a domestic conflagration in Japan some ten years ago, I've occasionally tried to recall one particular author who wrote in the 1900s about Lyndon words / strings, or ...
- 10.5k
11
votes
5
answers
506
views
What are efficient pooling designs for RT-PCR tests?
I realize this is long, but hopefully I think it may be worth the reading for people interested in combinatorics and it might prove important to Covid-19 testing. Slightly reduced in edit.
The ...
- 14.4k
2
votes
0
answers
159
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The topological complexity of polytopes
Polytopes arise naturally when modelling fundamental structures in Biology such as RNA and proteins [1,2]. Recently, it occurred to me that a complexity measure on the topology of polytopes might be ...
- 3,871
2
votes
1
answer
120
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Probability distributions with irregular behaviour
Might there be a probability distribution $\mathcal{D}$ such that if we sample $a_i \sim \mathcal{D}([-N,N])$ where $[-N,N] \subset \mathbb{Z}$ then if we define the asymptotic estimate $f$:
\begin{...
- 3,871
4
votes
1
answer
88
views
Separate a special poset by function
Assume $A = \prod_{i=1}^n\{0,1\}$, i.e. element $(a_1,\cdots,a_n)=a\in A$ is n-tuples like $(1,0,1,\cdots)$.
There is an obvious partial order on the $A$: say $a < b$ for $a,b\in A$ if and only ...
- 53
4
votes
3
answers
340
views
Relation between diametral path and regularity of a graph
Let $G(V,E)$ be a graph. A path whose length is equal to the diameter of a graph is called a diametral path. In a cycle graph every vertex has $2$ diametral paths. Now I need to prove that this:
If ...
13
votes
3
answers
2k
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Models for graphs representing real-life networks
I am interested in basic models of graphs (stochastic or deterministic) that are offered for real-life networks (like social networks, the Internet, neuron networks).
I will be thankful for answers ...
- 24.7k
0
votes
1
answer
118
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Comparing ideals in posets
Consider a partially ordered set $P$, and two upper sets $U_1$, $U_2$ in this poset.
What are some natural ways to measure how equal these two upper sets are?
This question arise naturally in the ...
- 15.8k
5
votes
2
answers
629
views
Average number of distinguished leaves in a binary tree
By a binary tree, I mean in this question a full rooted binary tree in which left and right child are labeled. A leaf of such a tree is a vertex of degree at most 1 (most references would probably ...
- 10.9k
2
votes
0
answers
215
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Number of breakpoints in parametric maximum flow problems
The parametric maximum flow problem can be formulated as
$$f(\lambda) = \min_{x\in\{0,1\}^n} \left( \sum_{i}(a_i + b_i\lambda)x_i + \sum_{i,j}c_{ij}x_ix_j \right),
$$
where all $c_{ij}<0$ (so that ...
- 567