Need help with Discrete Math
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I really hope someone here knows a bit about discrete math. Here's my problem: A standard notation for the number of partitions of an n-element set into k classes is S(n, k). Because the empty family of subsets of the empty set is a partition of the empty set, S(0, 0) is 1. In addition, S(n, 0) is 0 for n > 0, because there are no partitions of a nonempty set into no parts. S(1, 1) is 1. A) Explain why S(n, n) is 1 for all n > 0. Explain why _S(n, 1)_is 1 for all n > 0. B) Explain why S(n, k) = S(n - 1, k - 1) + kS(n - 1, k) for 1 < k < n. C) Make a table like Table 1.1 that shows the values of S(n, k) for values of n and k ranging from 1 to 6. Table 1.1 is [Pascal's triangle]. I'm not asking you guys to DO my homework. I'm just asking for some help with this one problem. Maybe some guidance as to what I should do. Thanks!
~ Tyler Candee About Me | Candee Computers
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I really hope someone here knows a bit about discrete math. Here's my problem: A standard notation for the number of partitions of an n-element set into k classes is S(n, k). Because the empty family of subsets of the empty set is a partition of the empty set, S(0, 0) is 1. In addition, S(n, 0) is 0 for n > 0, because there are no partitions of a nonempty set into no parts. S(1, 1) is 1. A) Explain why S(n, n) is 1 for all n > 0. Explain why _S(n, 1)_is 1 for all n > 0. B) Explain why S(n, k) = S(n - 1, k - 1) + kS(n - 1, k) for 1 < k < n. C) Make a table like Table 1.1 that shows the values of S(n, k) for values of n and k ranging from 1 to 6. Table 1.1 is [Pascal's triangle]. I'm not asking you guys to DO my homework. I'm just asking for some help with this one problem. Maybe some guidance as to what I should do. Thanks!
~ Tyler Candee About Me | Candee Computers
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That's a mathematics question, whereas this site is for programming questions.
Use the best guess
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I really hope someone here knows a bit about discrete math. Here's my problem: A standard notation for the number of partitions of an n-element set into k classes is S(n, k). Because the empty family of subsets of the empty set is a partition of the empty set, S(0, 0) is 1. In addition, S(n, 0) is 0 for n > 0, because there are no partitions of a nonempty set into no parts. S(1, 1) is 1. A) Explain why S(n, n) is 1 for all n > 0. Explain why _S(n, 1)_is 1 for all n > 0. B) Explain why S(n, k) = S(n - 1, k - 1) + kS(n - 1, k) for 1 < k < n. C) Make a table like Table 1.1 that shows the values of S(n, k) for values of n and k ranging from 1 to 6. Table 1.1 is [Pascal's triangle]. I'm not asking you guys to DO my homework. I'm just asking for some help with this one problem. Maybe some guidance as to what I should do. Thanks!
~ Tyler Candee About Me | Candee Computers
Its quite tricky, but try to post this question at likeplum. I always get good answers there to my computer/programming issues and questions. They have programmers online to help you now. You can get a great answer to your question so fast. https://www.likeplum.com/help/programming?aid=3321