Question

4. {10 marks} • Let A be the set of compositions where every part is in {3, 6} and if the composition is non-empty then the first part is 6. • Let B be the set of compositions where every part is at least 6 and is congruent to 6 (mod 3). (a) Write a set description for A. Determine the generating series ?A(x) with respect to the usual weight function (size) using sum/product/string lemmas. (b) Write a set description for B. Determine the generating series ?B(x) with respect to the usual weight function (size) using sum/product/string lemmas. (c) Give a bijection f from A and B that preserves size. Give its inverse g from B to A.

          4. {10 marks}
• Let A be the set of compositions where every part is in {3, 6} and if the composition is non-empty then the first part is 6.
• Let B be the set of compositions where every part is at least 6 and is congruent to 6 (mod 3).
(a) Write a set description for A. Determine the generating series ?A(x) with respect to the usual weight function (size) using sum/product/string lemmas.
(b) Write a set description for B. Determine the generating series ?B(x) with respect to the usual weight function (size) using sum/product/string lemmas.
(c) Give a bijection f from A and B that preserves size. Give its inverse g from B to A.

4. 10 marks
• Let A be the set of compositions where every part is in 3, 6 and if the composition is non-empty then the first part is 6.
• Let B be the set of compositions where every part is at least 6 and is congruent to 6 (mod 3).
(a) Write a set description for A. Determine the generating series ?A(x) with respect to the usual weight function (size) using sum/product/string lemmas.
(b) Write a set description for B. Determine the generating series ?B(x) with respect to the usual weight function (size) using sum/product/string lemmas.
(c) Give a bijection f from A and B that preserves size. Give its inverse g from B to A.

Added by Caleb P.

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