#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 studied them, but the first construction was a 4 x 4 set published by Jacques Ozanam in 1725.

A latin square is an n × n array filled with n different symbols, each occurring exactly once in each row and exactly once in each column.

A latin-greco square is an n × n arrangement of cells, each cell containing an ordered pair (s, t), where s is in S and t is in T, such that every row and every column contains each element of S and each element of T exactly once, and that no two cells contain the same ordered pair.

(credits to wikipedia)

2) What is nops(AllGraphs(20));
2^(20*(20-1)/2) =1569275433846670190958947355801916604025588861116008628224

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

4) Is this sequence in the oeis? If it is what is its a-number?
What is the description?
{1,1,4,38,728}

Yes, it is A001187. It is the number of connected labeled graphs with n nodes.

5) Draw G manually

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

6) [1,1,3,16,125,1296]
Is this seuqnece in the oeis? Yes
What is the A-number? A000272
What is the number of labeled trees with 20 vertices?
20^18 = 262144000000000000000000

7) [1,15,222,3660]
Is this in the oeis? Yes
What is the a-number, reason?
A057500, it is the number of connected labeled graphs with n edges and n nodes. 

8) [6,205,5700]
Is this in the oeis? A-number?
Yes, A061540