Extra Credit assignment: Catalan numbers (solutions)
Lewis Bowen
Texas A&M University
October 22, 2011
Note. To get credit, this has to be turned in by 10/18/11. The maximum possible credit
is 3% added to your total score at the end of the semester.
The C
Extra Credit assignment: Counting labeled graphs
Lewis Bowen
Texas A&M University
October 22, 2011
Note. To get credit, this has to be turned in by 11/15/11. The maximum possible credit
is 2% added to your total score at the end of the semester.
The purpo
Exam 1
Instructions: Show all of your work. It is OK to leave your answer in terms of binomial
coecients, multinomial coecients, Stirling numbers, partition numbers and so on. Calculators and notes are not allowed.
Formulas
1. xn =
n
k=0
2. (x + y )n =
S
Practice for Exam 2
Instructions: Show all of your work. It is OK to leave your answer in terms of binomial
coecients, multinomial coecients, Stirling numbers, partition numbers and so on. Calculators and notes are not allowed. The exam covers chapters 6-
Practice for the Final
Instructions: Show all of your work. It is OK to leave your answer in terms of binomial
coecients, multinomial coecients, Stirling numbers, partition numbers and so on. Calculators and notes are not allowed.
Formulas
1. The number o