Sterling numbers of the First kind Combinatorial Proof

In summary, the conversation discusses calculating sterling numbers of the first kind for a specific scenario, where n people are seated at n-2 circular tables and 2 remaining people can be seated at any of the tables. The conversation ends with one person asking for clarification and the other expressing difficulty in finding a solution.
  • #1
silvermane
Gold Member
117
0

Homework Statement


Say we have sterling numbers of the first kind where we're given s(n, n-2) = 2(nC3) + 3(nC4)
for n greater than or equal to 4.

The Attempt at a Solution


So, for the left side, we have n people, and we wish to seat them at n-2 circular tables, where if we first seat n-2 people, we'll have 2 remaining people to sit down at any of the n-2 circular tables. I just want to know if I'm on the right track here; thank you so much for your time!
 
Physics news on Phys.org
  • #2
Hey, I was wondering if you figured out a solution to this and remember it? I can't figure it out at all!
 

What are Sterling numbers of the First kind?

Sterling numbers of the First kind, denoted as s(n, k), are combinatorial numbers that represent the number of ways to partition a set of n elements into k non-empty cycles. They are used in combinatorics, number theory, and algebraic topology.

What is a Combinatorial Proof?

A combinatorial proof is a type of mathematical proof that uses counting techniques and combinatorial arguments to prove the validity of a mathematical statement. It relies on the principle that two different ways of counting the same thing must give the same result.

How are Sterling numbers of the First kind calculated?

Sterling numbers of the First kind can be calculated using a recursive formula or through a table of values. The recursive formula is s(n, k) = s(n-1, k-1) + (n-1)*s(n-1, k), where s(n, k) represents the number of ways to partition a set of n elements into k non-empty cycles.

What is the significance of Sterling numbers of the First kind?

Sterling numbers of the First kind have various applications in mathematics, including determining the number of equivalence relations on a set, calculating the number of ways to divide a set of objects into subsets, and solving problems in algebraic topology.

What are some real-life examples of Sterling numbers of the First kind?

Sterling numbers of the First kind can be used to model social networks, where n represents the number of people and k represents the number of social groups. They can also be applied in genetics, where n represents the number of genes and k represents the number of genetic traits.

Similar threads

How Do Stirling Numbers of the First Kind Relate to Combinatorial Formulas?
    • Calculus and Beyond Homework Help
Replies
1
Views
1K
Each integer n>11 can be written as the sum of two composite numbers?
    • Calculus and Beyond Homework Help
Replies
7
Views
2K
Prove ##(a+b)\cdot c=a\cdot c+b\cdot c## using Peano postulates
    • Calculus and Beyond Homework Help
Replies
3
Views
521
Statistics Permutations and Combinations
    • Calculus and Beyond Homework Help
Replies
8
Views
3K
Proof of uniqueness of limits for a sequence of real numbers
    • Calculus and Beyond Homework Help
Replies
13
Views
2K
Proof of an inequality with natural numbers
    • Calculus and Beyond Homework Help
Replies
3
Views
1K
Understanding the meaning of "expected fraction" (Statistics)
    • Calculus and Beyond Homework Help
Replies
4
Views
1K
How Does Choosing N Affect Limit Proofs in Calculus?
    • Calculus and Beyond Homework Help
Replies
12
Views
908
Proof that algebraic numbers are countable
    • Calculus and Beyond Homework Help
Replies
6
Views
2K
Changing the Statement Combinatorial proofs & Contraposition
    • Math Proof Training and Practice
Replies
5
Views
814

Hot Threads

Recent Insights

Back
Top