(a) Show that the number of paths from (0,0) to (n, m) takingsteps of size (0,1) or (1,0) is ("m").(b) Show that the number of integer partitions (of any size) with at most n parts and with largest part ofsize at most m equals ("+").

Since the second question is independent of the first question, as per the guidelines I am answering…

(a) Show that the number of paths from (0,0) to (n, m) taking steps of size (0,1) or (1,0) is (""). Show that the number of integer partitions (of any size) with at most n narts and with largest part of

(a) Show that the number of paths from (0,0) to (n, m) taking steps of size (0,1) or (1,0) is (""). Show that the number of integer partitions (of any size) with at most n narts and with largest part of

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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Question

(a) Show that the number of paths from (0,0) to (n, m) taking
steps of size (0,1) or (1,0) is ("m").
(b) Show that the number of integer partitions (of any size) with at most n parts and with largest part of
size at most m equals ("+").

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