Introductory Combinatorics
Introductory Combinatorics
5th Edition
ISBN: 9780136020400
Author: Richard A. Brualdi
Publisher: Prentice Hall
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Chapter 7, Problem 49E
To determine

To prove: That the q-binomial theorem (x+y)(x+qy)(x+q2y)...(x+qn1y)=k=0n(nk)qxnkyk, where n!q=j=1n1qj(1q)n is the q- factorial and (nk)q=n!qk!q(nk)!q is the q-binomial coefficient.

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Chapter 7 Solutions

Introductory Combinatorics

Ch. 7 - Prob. 11ECh. 7 - Prob. 12ECh. 7 - 13. Determine the generating function for each of...Ch. 7 - 14. Let S be the multiset {∞ · e1, ∞ · e2, ∞ · e3,...Ch. 7 - 15. Determine the generating function for the...Ch. 7 - 16. Formulate a combinatorial problem for which...Ch. 7 - 17. Determine the generating function for the...Ch. 7 - 18. Determine the generating function for the...Ch. 7 - 19. Let h0, h1, h2, …, hn, … be the sequence...Ch. 7 - Prob. 20ECh. 7 - 21. * Let hn denote the number of regions into...Ch. 7 - 22. Determine the exponential generating function...Ch. 7 - 23. Let α be a real number. Let the sequence h0,...Ch. 7 - 24. Let S be the multiset {∞ · e1, ∞ · e2, · , ∞ ·...Ch. 7 - 25. Let hn denote the number of ways to color the...Ch. 7 - Determine the number of ways to color the squares...Ch. 7 - Determine the number of n-digit numbers with all...Ch. 7 - Determine the number of n-digit numbers with all...Ch. 7 - We have used exponential generating functions to...Ch. 7 - Prob. 30ECh. 7 - Solve the recurrence relation hn = 4hn−2, (n ≥ 2)...Ch. 7 - Prob. 32ECh. 7 - Solve the recurrence relation hn = hn−1 + 9hn−2 −...Ch. 7 - Solve the recurrence relation hn = 8hn−1 − 16hn−2,...Ch. 7 - Solve the recurrence relation hn = 3hn − 2 − 2hn −...Ch. 7 - Prob. 36ECh. 7 - Determine a recurrence relation for the number an...Ch. 7 - Prob. 38ECh. 7 - Let hn denote the number of ways to perfectly...Ch. 7 - Let an equal the number of ternary strings of...Ch. 7 - * Let 2n equally spaced points be chosen on a...Ch. 7 - Solve the nonhomogeneous recurrence relation Ch. 7 - Solve the nonhomogeneous recurrence relation hn =...Ch. 7 - Solve the nonhomogeneous recurrence relation Ch. 7 - Prob. 45ECh. 7 - Solve the nonhomogeneous recurrence relation Ch. 7 - Solve the nonhomogeneous recurrence relation Ch. 7 - Solve the following recurrence relations by using...Ch. 7 - (q-binomial theorem) Prove that where is the...Ch. 7 - Call a subset S of the integers {1, 2, …, n}...Ch. 7 - Solve the recurrence relation from Section 7.6...Ch. 7 - Prob. 52ECh. 7 - Suppose you deposit $500 in a bank account that...
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