#ATTENDANCE QUIZ FOR LECTURE 18 of Dr. Z.'s Math454(02) Rutgers University

# Please Edit this .txt page with Answers

#Email  ShaloshBEkhad@gmail.com 
#Subject: p18
#with an attachment called
#p18FirstLast.txt
#(e.g. p18DoronZeilberger.txt)

#Right after finishing watching the lecture but no later than Nov. 10, 2020, 8:00pm


THE NUMBER OF ATTENDANCE QUESTIONS WERE: 8

PLEASE LIST ALL THE QUESTIONS FOLLOWED, AFTER EACH, BY THE ANSWER

1. Who invented latin squares and latin-greco squares, and what are they?
Euler invented latin and and latin-greco squares. A latin square is an nxn array filled with n different symbols, where each symbol can occur exactly once in each row and column.

2. What is nops(AllGraphs(20))?
2^20

3. What is CC(G,38)?
{1,38}

4. Is this sequence in the OEIS? If it is what is the A number?
Yes, the sequence [1,1,4,38,728] is in the OEIS. The A number is A001187, and the sequence describes the number of connected graphs with n nodes.

5. Draw this graph manually.
[{4,8},{7},{5,9},{1,6},{3,7,10},{4,9},{2,5},{1},{3,6},{5}]

1-4-6-9-3-5-7-2
|         |
8         10

6.
i. Is this sequence in the OEIS?
Yes, the sequence [1,1,3,16,125,1296] is in the OEIS.
ii. What is the A number?
The A number is A000272.
iii. What is the number of (labeled) trees with 20 vertices?
There are 262144000000000000000000 trees with 20 vertices.

7. Is this sequence in the OEIS? What is the A-number, reason?
Yes, the sequence [1,5,22,3660] is in the OEIS. The A number is A057500, and the sequence describes the number of connected labeled graphs with n edges and n nodes.

8. Is this sequence in the OEIS? A-number?
Yes, the sequence [6,205,5700] is in the OEIS. The A number is A061540, and the sequence describes the number of connected labeled graphs with n nodes and n+1 edges.