- Math 192r, Problem Set #2: Solutions 1. Find necessary and sufficient conditions for the infinite product f1f2f3
- Math 192r, Problem Set #17 (due 11/29/01)
- Math 192r, Problem Set #9 (solutions) 1. For various small values of n (1 through 5, at least), determine the
- Solution to Problem 10877 from the American Mathematical Monthly
- Math 192r, Problem Set #19 (due 12/6/01)
- Math 192r, Problem Set #21: Solutions 1. For n 0 let A(n) = n/2kn 2k
- A Reciprocity Sequence for Perfect Matchings of Linearly Growing Graphs David Speyer, Undergraduate at Harvard University, speyer@fas.harvard.edu
- Lattice animals and heaps of dimers Mireille Bousquet-M elou
- Math 192r, Problem Set #18: Solutions 1. (from unpublished work of Douglas Zare) Let G m;n be the directed graph
- Math 192r, Problem Set #6: Solutions 1. For each even integer n 2, we can represent each domino tiling of a
- Math 192r, Problem Set #7 (due 10/11/01)
- Math 192r, Problem Set #19: Solutions 1. In problem #3 of assignment #17, multivariate polynomials
- Math 192r, Problem Set #4: Solutions Let a n be the number of domino tilings of a 3-by-2n rectangle, and let b n be
- Math 192r, Problem Set #20: Solutions 1. Let f( ) be some polynomial (in one variable), and de ne a sequence
- Math 192r, Problem Set #17 --Solutions 1. Let P(n) and Q(n) denote the numerator and denominator obtained
- Math 192r, Problem Set #16: Solutions 1. Use Dodgson condensation to prove the Vandermonde determinant for-
- Math 192r, Problem Set #21: Solutions 1. For n 0 let A(n) = P
- Math 192r, Problem Set #17 | Solutions 1. Let P (n) and Q(n) denote the numerator and denominator obtained
- Math 192r, Problem Set #3: Solutions 1. Let F n be the nth Fibonacci number, as Wilf indexes them (with F 0 =
- Math 192r, Problem Set #20 (due 12/11/01)
- Math 192r, Problem Set #19 (due 12/6/01)
- Math 192r, Problem Set #15: Solutions 1. Using the combinatorial de nition of the determinant, prove that for
- Math 192r, Problem Set #7 (Solutions) 1. (a) How many di erent polygonal paths of length n are there that start
- Math 192r, Problem Set #13: Solutions 1. (a) How many lattice paths from (0, 0) to (m, n) remain the same when
- Math 192r, Problem Set #12 (due 11/6/01)
- Math 192r, Problem Set #11: Solutions 1. An \augmented Aztec diamond of order n" is a subset of the square grid
- Math 192r, Problem Set #2: Solutions 1. Find necessary and sucient conditions for the in nite product f 1 f 2 f 3
- Math 192r, Problem Set #14: Solutions 1. Use the recurrence for p(n) to compute the last digit of p(n) for ev-
- Math 192r, Problem Set #9 (solutions) 1. For various small values of n (1 through 5, at least), determine the
- Math 192r, Problem Set #8: Solutions 1. De ne the diagonal of a two-variable generating function
- Math 192r, Problem Set #1: Solutions 1. (a) Write and run a program to compute f(n) = P n
- Math 192r, Problem Set #19: Solutions 1. In problem #3 of assignment #17, multivariate polynomials
- Math 192r, Problem Set #14: Solutions 1. Use the recurrence for p(n) to compute the last digit of p(n) for ev-
- Math 192r, Problem Set #5: Solutions 1. There is a unique polynomial of degree d such that f(k) = 2 k for k =
- Math 192r, Problem Set #10 (due 10/23/01)
- Math 192r, Problem Set #16: Solutions 1. Use Dodgson condensation to prove the Vandermonde determinant for-
- Math 192r, Problem Set #6: Solutions 1. For each even integer n 2, we can represent each domino tiling of a
- Math 192r, Problem Set #12: Solutions 1. We consider directed animals on the modified square lattice that has
- Math 192r, Problem Set #11: Solutions 1. An "augmented Aztec diamond of order n" is a subset of the square grid
- Math 192r, Problem Set #4: Solutions Let an be the number of domino tilings of a 3-by-2n rectangle, and let bn be
- Math 192r, Problem Set #9 (due 10/18/01)
- Math 192r, Problem Set #1: Solutions 1. (a) Write and run a program to compute f(n) = n
- Discrete analogue computing with rotor-routers
- ?W H A T I S . . . a Sandpile?
- Math 192r, Problem Set #3: Solutions 1. Let Fn be the nth Fibonacci number, as Wilf indexes them (with F0 =
- Math 192r, Problem Set #5: Solutions 1. There is a unique polynomial of degree d such that f(k) = 2k
- Math 192r, Problem Set #7 (due 10/11/01)
- Math 192r, Problem Set #7 (Solutions) 1. (a) How many different polygonal paths of length n are there that start
- Math 192r, Problem Set #8: Solutions 1. Define the diagonal of a two-variable generating function
- Math 192r, Problem Set #10 (due 10/23/01)
- Math 192r, Problem Set #10: Solutions 1. Using a sign-reversing involution, prove that for all n > k, the sum
- Math 192r, Problem Set #15: Solutions 1. Using the combinatorial definition of the determinant, prove that for
- Math 192r, Problem Set #18 (due 12/4/01)
- Math 192r, Problem Set #18: Solutions 1. (from unpublished work of Douglas Zare) Let Gm,n be the directed graph
- Math 192r, Problem Set #20 (due 12/11/01)
- Math 192r, Problem Set #20: Solutions 1. Let f() be some polynomial (in one variable), and define a sequence
- Math 192r, Problem Set #17 (due 11/29/01)
- Solution to Problem 10877 of The American Mathematical Bridget Eileen Tenner
- Math 192r, Problem Set #13: Solutions 1. (a) How many lattice paths from (0; 0) to (m; n) remain the same when
- Math 192r, Problem Set #9 (due 10/18/01)
- Math 192r, Problem Set #18 (due 12/4/01)
- Math 192r, Problem Set #10: Solutions 1. Using a sign-reversing involution, prove that for all n > k, the sum
- Math 192r, Problem Set #12: Solutions 1. We consider directed animals on the modi ed square lattice that has
