#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



#ATTENDANCE Q. #1 for LECTURE 18
#Who invented latin squares and latin-greco squares, and what are they?

#ANSWER to Q. #1:	

# Leonhard Euler.  A latin square is an nxn array filled with n different items, each occuring exactly
# once in each row and column (Wikipedia)
# A Graeco-latin square is a pair of two latin squares such that then one is laid on top of the other
# every ordered pair of symbols appears only once




#ATTENDANCE Q. #2 for LECTURE 18
#What is nops(AllGraphs(20))?

#ANSWER to Q. #2:

#it seems to follow a pattern like 1,2,8,64,1024... which on the OEIS is a(n) = 2^(n*(n-1)/2)
#Doing 2^(20*19/2) = 2^190 = 1569275433846670190958947355801916604025588861116008628224




#ATTENDANCE Q. #3 for LECTURE 18
#What is CC(G,38)?

#ANSWER to Q. #3:

#I got {1,38}




#ATTENDANCE Q. #4 for LECTURE 18
#Is [1,1,4,38,728...] in the oeis? A number?

#ANSWER to Q. #4:

#Yes, its A number is A001187 "Number of connected labeled graphs with n nodes."




#ATTENDANCE Q. #5 for LECTURE 18
#Draw this graph manually 8-1-4-6-9 (finish it)

#ANSWER to Q. #5:

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




#ATTENDANCE Q. #6 for LECTURE 18
#Is this sequence in the OEIS (1 1 3 16 125 1296)? A number? Number of (labeled) trees with 20 vertices?

#ANSWER to Q. #6:

#Yes, A000272, there are 20^18 trees




#ATTENDANCE Q. #7 for LECTURE 18
#Is this sequence in the OEIS (1 15 222 3660)? A number? reason?

#ANSWER to Q. #7:

#Yes, A057500	"Number of connected labeled graphs with n edges and n nodes."




#ATTENDANCE Q. #8 for LECTURE 18
#Is this sequence in the OEIS [6, 205, 5700]? A number?

#ANSWER to Q. #8:

#Yes, A061540