8. In Mathematics, a composition of an integer n is a way of writing n as...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
8. In Mathematics, a composition of an integer n is a way of writing n as the sum of a sequence of (strictly) positive integers. Two sequences that differ in the order of their terms define different compositions of their sum, while they are considered to define the same partition of that number. (a) Show that the number of compositions of n into exactly k parts is (-1). [5 marks] (b) Let pa(n, k) be the number of partitions of n into k distinct parts. Show that [8 marks] 1 n- pa(n, k) < ² (^= 1) = ≤ Pk (n) k! k- (c) Let m = n + (₂). Show that [7 marks] Pu(n) ≤ / 1 (n=1). k! k -1 8. In Mathematics, a composition of an integer n is a way of writing n as the sum of a sequence of (strictly) positive integers. Two sequences that differ in the order of their terms define different compositions of their sum, while they are considered to define the same partition of that number. (a) Show that the number of compositions of n into exactly k parts is (-1). [5 marks] (b) Let pa(n, k) be the number of partitions of n into k distinct parts. Show that [8 marks] 1 n- pa(n, k) < ² (^= 1) = ≤ Pk (n) k! k- (c) Let m = n + (₂). Show that [7 marks] Pu(n) ≤ / 1 (n=1). k! k -1
Expert Answer:
Answer rating: 100% (QA)
S C Comportion of 0 No So Firstly 5 5 integer of Compositi... View the full answer
Related Book For
Posted Date:
Students also viewed these accounting questions
-
Explain how two sequences that differ only in their first ten terms can have the same limit.
-
For any integer k > 0, an integer n is a kth power if there exists an integer a such that a k = n. Furthermore, n > 1 is a nontrivial power if it is a kth power for some integer k > 1. Show how to...
-
(a) An integer N is to be selected at random from {1, 2, . . . , (10)3} in the sense that each integer has the same probability of being selected. What is the probability that N will be divisible by...
-
The homogeneous rectangular block having dimensions a-1.93, b=2.75 as shown, and mass m, rests on the inclined plane which is hinged about a horizontal axis through O. Calculate the minimum value of...
-
Use the information in the following stock quote to calculate Abercrombie & Fitchs earnings per share over the last year. (2 (3) 4(5) (6 (7) ( (9 (10 et %Chg Volume Chg (12) (13 14 (15) YTD 52 week...
-
The step response of a linear circuit is \(g(t)=0.5\) [1\(\left.e^{-250 t}ight] u(t)\). Find the output waveform when the input is \(v_{1}(\) \(t)=\left[20 e^{-200 t}ight] u(t)\). Use MATLAB to find...
-
The Cooper Furniture Company of Potomac, Maryland, assembles two types of chairs (Recliners and Rockers). Separate assembly lines are used for each type of chair. Classify each cost item (AI) as...
-
Journal Entries for Fair Value and Equity Methods Presented below are two independent situations. Situation 1 Hatcher Cosmetics acquired 10% of the 200,000 shares of common stock of Ramirez Fashion...
-
Fort Gaines guards the western entrance to Mobile Bay. In order to prevent enemy ships from passing, it needs to be able to cover about 1 km of the bay with cannon fire. The cannons fire projectiles...
-
Baer Belly Bikinis, Inc. (BBB) is a small business located in Santa Monica, California. It sells swimwear and related products to specialty stores throughout the United States. It also sells its...
-
On January 1, 2017, Grand Haven, Inc., reports net assets of $933,650 although equipment (with a four-year remaining life) having a book value of $536,000 is worth $598,250 and an unrecorded patent...
-
Explain why German reparation payments were essential to the survival of the international financial system in the 1920s
-
Explain the concept of inflation in your own terms. How have you been impacted by inflation in your lifetime? What did you do to offset the rising costs?
-
Elucidate the interconnection between labeling theory and symbolic interaction theory, highlighting their conceptual synergy. Additionally, furnish an illustrative example demonstrating the...
-
Fanblade, Inc. is a manufacturer of fan blades for jet engines. These blades are where cool air ranging from -50oC to +50oC enters the jet engine. The fan blades are exposed to foreign objects such...
-
Zoe (Gemma's replacement - how quickly is Gemma replaced? Brutal!) raises concerns with the partner, Will, about: irregularities with the purchase of artwork the tax issue irregularities with the...
-
1. Define and discuss the Order Management System. Discuss how the Internet has affected the Order to Cash cycle. 2. There are two options for product flow through the supply chain: direct shipments...
-
For the following exercises, rewrite the sum as a product of two functions or the product as a sum of two functions. Give your answer in terms of sines and cosines. Then evaluate the final answer...
-
Let X be such that P{X = 1} = p = 1 P{X = 1} Find c 1 such that E[cX] = 1.
-
Five people, designated as A, B, C, D, E, are arranged in linear order. Assuming that each possible order is equally likely, what is the probability that (a) There is exactly one person between A and...
-
Show that the jointly continuous (discrete) random variables X1, . . . ,Xn are independent if and only if their joint probability density (mass) function f (x1, . . . , xn) can be written as for...
-
Visit the Suzy Lamplugh Trust website at http://www.suzylamplugh.org and the Social Research Association at http://the-sra.org.uk/sra_resources/safety-code/ . Browse the guidance leaflets/web pages...
-
Andrew, a final year part-time MBA student employed by a large Maltese market research company, read in a local newspaper that Malta (a small island state situated in the centre of the Mediterranean...
-
Maria had a problem. The research proposal for her masters research project was due. But she had no idea what to research. Sustainable tourism had been her favourite module on the programme and...
Study smarter with the SolutionInn App