maths.free › Probability Theory › Applying Probability to Combinatorics › Estimating Ramsey Numbers
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: \[\begin{aligned}\end{aligned}\]
Nu er du Ingen lommeregner afgør dette, men stykkerne af det er komputerbare. Prøv en nedenfor, eller skriv din egen.
En gratis konto tilføjer noter om hver lektion, en rekord over, hvad du har afsluttet, dine løste problemer på ét sted, og en vejleder, du kan spørge om denne side. Matematik selv er åben for alle, logget på eller ej.
Tilmeld dig LoginSymboler brugt her
Tryk på ethvert symbol for den fulde definition, et billede, og hvad hvert bogstav i det betyder.
Spørgsmål folk spørger
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.
Dele af denne side er tilpasset fra Keller & Trotter, Applied Combinatorics (CC BY-SA 4.0). Kondenseret og genforklaret her; fejl er vores.
Mere i Probability Theory
Sample spaces and the axiomsRandom variables and expectationThe common distributionsThe law of large numbers and the central limit theorem