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1. Let P₁ denote the set of partitions, which are finite sequences of decreasing positive integers summing up to n. For instance, Ps= {(4), (3, 1), (2, 2), (2, 1, 1), (1, 1, 1, 1)}. On the other hand, let Y, be the set of diagrams D of size n which are collections of n boxes in the first quadrant that are stacked, as if "grav- ity" is pulling them down and to the left. For instance, the set Y₂ is: 0888 (a) List the elements of P, and Y5. (b) Describe a bijection between P4 and Y₁, and illustrate it for n = 5.

1. Let P₁ denote the set of partitions, which are finite sequences of decreasing positive integers summing up to n. For instance, Ps= {(4), (3, 1), (2, 2), (2, 1, 1), (1, 1, 1, 1)}. On the other hand, let Y, be the set of diagrams D of size n which are collections of n boxes in the first quadrant that are stacked, as if "grav- ity" is pulling them down and to the left. For instance, the set Y₂ is: 0888 (a) List the elements of P, and Y5. (b) Describe a bijection between P4 and Y₁, and illustrate it for n = 5.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. Let Pn denote the set of partitions, which are finite sequences of decreasing positive integers summing up to n. For instance, P = {(4), (3, 1), (2, 2), (2, 1, 1), (1, 1, 1, 1)}. On the other hand, let Y₁, be the set of diagrams D of size n which are collections of n boxes in the first quadrant that are stacked, as if "grav- ity" is pulling them down and to the left. For instance, the set Y₂ is: (a) List the elements of P, and Y5. (b) Describe a bijection between P4 and Y₁, and illustrate it for n = 5.
Transcribed Image Text:1. Let Pn denote the set of partitions, which are finite sequences of decreasing positive integers summing up to n. For instance, P = {(4), (3, 1), (2, 2), (2, 1, 1), (1, 1, 1, 1)}. On the other hand, let Y₁, be the set of diagrams D of size n which are collections of n boxes in the first quadrant that are stacked, as if "grav- ity" is pulling them down and to the left. For instance, the set Y₂ is: (a) List the elements of P, and Y5. (b) Describe a bijection between P4 and Y₁, and illustrate it for n = 5.
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