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# hw5 - Math 146 Algebraic Combinatorics Homework 5 This...

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Math 146: Algebraic Combinatorics Homework 5 This problem set is due Friday, April 30. Do problem *3.1 and 3.21, in addition to my problems. A remark on where we are in the book: We’re sort-of in sections 2.3 and 2.4, but we also did sections 3.14 and 3.15, and I will say some things about partitions as covered in 3.16. A hint on problem 3.1, which is quite difficult otherwise: Given a partition on n into odd parts, you can center its Ferrers diagram. Then you can divide the centered diagram into L shapes, which is then a partition of the same n into distinct parts. For example, given 18 = 7 + 5 + 3 + 3, the centered diagram is to yield 18 = 7 + 6 + 4 + 1. You should describe more rigorously what the L shapes do, and prove that it is a bijection between the two types of partitions. Update: I decided to make problem 3.1 extra credit. GK5.1 The partition number p ( n ) in section 3.16 can be described as the number of ways to express n cents with unordered coins, with one coin of each denomination 1 cent, 2 cents, 3 cents, etc. Suppose instead that the coins are ordered, or that we are looking at ordered partitions where 3 = 2 + 1 is different from 3 = 1 + 2. Let’s call the number of such partitions

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hw5 - Math 146 Algebraic Combinatorics Homework 5 This...

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