#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


# Question 1: Who invented Latin Squares and Latin-Greco Squares, and what are they?

# Answer: Leonhard Euler.
# 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.

# An   N x N   Graeco-Latin Square involves two sets of N elements. We put one
# element from the first set and an element from the second set in each box, so that no
# two pairs are the same (equivalently, so that all N^2 possible pairs appear in the array),
# and such that in each row, and in each column, all the 2N elements are different.

# Question 2: What is nops(AllGraphs(20))

# Answer: 2^(20 Choose 2). There are (20 Choose 2) edges and we can either include it or not use it. 

# Question 3: What is CC(G,38)?

# Answer: {1, 38}

# Question 4: Is this sequence in the OEIS ([1,1,4,38,728])? If it is, what is its A-Number? 

# Answer: A001187 - Number of connected labeled graphs with n nodes.

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

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

# Question 6:
# (i) Is this sequence ([1,1,3,16,125,1296]) in the OEIS?
# (ii) What is the A-Number
# (iii) What is the number of (labelled) trees with 20 vertices?

# Answer:
# A000272: Number of trees on n labeled nodes: n^(n-2) with a(0)=1.
# The number of labelled trees with 20 vertices is 20^(20-2) = 262144000000000000000000

# Question 7: Is this in the OEIS ([1,15,222,3660])? What is the A-Number, reason?

# Answer:
# A057500 - Number of connected labeled graphs with n edges and n nodes.

# Question 8: Is [6,205,5700] in the OEIS? A-Number?

# Answer:
# A061540 - Number of connected labeled graphs with n nodes and n+1 edges.