Binomial Coefficients and Generating Functions - Cs.ioc.ee

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Pascal’s Triangle n 0 n 0 1 n 1 n 2 n 3 n 4 n 5 n 6 1 1 1 2 1 2 1 3 1 3 3 1 4 1 4 6 4 1 5 1 5 10 10 5 1 6 1 6 15 20 15 6 1 Blaise Pascal (1623–1662)
Pascal’s Triangle 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 Pascal Triangle is symmetric with respect to the vertical line through its apex. Blaise Pascal (1623–1662) Every number is the sum of the two numbers immediately above it.
Page 1 and 2: Binomial Coefficients and Generatin
Page 3 and 4: Next section 1 Binomial coefficient
Page 5 and 6: Binomial coefficients and combinati
Page 7 and 8: Properties of Binomial Coefficients
Page 9: Yet Another Proerty 4 If n,k > 0, t
Page 13 and 14: Next section 1 Binomial coefficient
Page 15 and 16: More examples (1) 〈1,1,1,1,...〉
Page 17 and 18: More examples (2) 〈a,ab,ab 2 ,ab
Page 19 and 20: More examples (3) Taking in the las
Page 21 and 22: Next subsection 1 Binomial coeffici
Page 23 and 24: Operations on Generating Functions
Page 35 and 36: Counting with Generating Functions
Page 37 and 38: Building Generating Functions that
Page 43 and 44: How many positive integer solutions
Page 45 and 46: How many positive integer solutions
Page 47 and 48: Number of solutions of the equation
Page 49 and 50: Distribute n objects into k bins so
Page 51 and 52: Example: 100 Euro How many ways 100
Page 53 and 54: Example: 100 Euro (2) 1. Observatio
Page 55 and 56: Example: 100 Euro (3) Convolution:
Page 57 and 58: Vandermonde’s identity Binomial t
Page 59 and 60: Vandermonde’s identity (2) Equati
Page 61 and 62:
Vandermonde’s identity (3) Specia
Page 63:
Some other useful sequences For any
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