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| ## Homework## Suggested practice problems, not collectedA. Show that classical Möbius inversion is a special case of poset Möbius inversion. n} which do not contain both +i and -i for any i. ## Homework 12, due Apr 30 at 1:07pmPlease do the following problems from the textbook:Bona, p397: 24, 29, 37, 40, 41, 45 Poset products (as in Problem 29) are Definition 16.23 in Bona. ## Homework 11, due Apr 23 at 1:07pmPlease do the following problems from the textbook:Bona, p366: 30a And the following additional problems: i in [n], and n random coinflips, then proceed as in the EKR Theorem. ## Homework 10, due Apr 16 at 1:07pmPlease do the following problems from the textbook: Bona, p260: 28 And the following additional problems: ## Homework 9, due Apr 9 at 1:07pmPlease do the following problems from the textbook:Bona, p260: 8, 24, 25, 26, 27 And the following additional problems: S._{i} . Give a short proof that Hall's Marriage Theorem implies Hall's SDR Theorem. ## Homework 8, due Apr 2 at 1:07pmPlease do the following problems from the textbook: Bona, p200: 29, 38, 39, 42 Note: Simple graph for us just means graph. The word 'simple' distinguished from graphs with "loops" and "multi-edges". ## Homework 7, due Mar 24 at 1:07pmPlease do the following problems from the textbook:Bona, p168: 10, 29 (just find the explicit formula), 32, 35, 44a Hint: It may be useful to consider ## Homework 6, due Mar 17 at 1:07pmPlease do the following problems from the textbook: Bona, p139: 27, 28+ And the following additional problems: ## Homework 5, due Mar 3 at 1:07pmPlease do the following problems from the textbook: Bona, p124: 45, 47, And the following additional problem: ## Homework 4, due Feb 24 at 1:07pmPlease do the following problems from the textbook:Bona, p122: 27, 29, 31, 38, 40 And the following additional problem: Note: In Problem 29, the ## Homework 3, due Feb 17 at 1:07pmPlease do the following problems from the textbook: Bona, p103: 28 for And the following additional problem: b_{1}, ..., b_{n}} of such that (R^{n}b_{i})A = _{p}b_{p(i)}, where A is as in problems 11 and 12, and the multiplication is of a row vector with _{p}A. _{p}## Homework 2, due Feb 10 at 1:07pmPlease do the following problems from the textbook: Bona, p77: 32, 50+, 52, 53 Hint on p77 #50: Try to set up a bijection with a certain subclass of lattice paths from (0, 0) to ( Note: there is an error in the text for #51. The number of sequences should be Catalan, i.e., ( 2 ## Homework 1, due Feb 3 at 1:07pmPlease do the following problems from the textbook: Bona, p51: 25, 27, 30, 33, 43, 48 (Note that there is an error in p77 #37 in earlier printings of the book.) And the following additional problem: Red text (like the plus sign in Problem A) reflect corrections made after the initial assignment. |