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Estimating Ramsey Numbers
We will find it convenient to utilize the following approximation due to Stirling. You can find a proof in almost any advanced calculus book.
Estimating Ramsey Numbers
We will find it convenient to utilize the following approximation due to Stirling. You can find a proof in almost any advanced calculus book. \[\begin{aligned}\end{aligned}\] Of course, we will normally be satisfied with the first term: \[\begin{aligned}\end{aligned}\] Using Stirling's approximation and the binomial coefficients from the proof of , we have the following upper bound: \[\begin{aligned}\end{aligned}\]
Now you No calculator settles this one, but the pieces of it are computable. Try one below, or type your own.
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Questions people ask
What is the difference between probability and statistics?
Probability goes from a known model to what the data should look like; statistics goes from data back to the model. Probability theory is the deductive half.
What does the law of large numbers promise?
That the average of many independent samples converges to the expected value. It says nothing about any single trial.
Parts of this page are adapted from Keller & Trotter, Applied Combinatorics (CC BY-SA 4.0). Condensed and re-explained here; errors are ours.
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Sample spaces and the axiomsRandom variables and expectationThe common distributionsThe law of large numbers and the central limit theorem