#ATTENDANCE QUIZ FOR LECTURE 20 of Dr. Z.'s Math454(02) Rutgers University

# Please Edit this .txt page with Answers

#Email  ShaloshBEkhad@gmail.com 
#Subject: p20
#with an attachment called
#p20FirstLast.txt
#(e.g. p19DoronZeilberger.txt)

#Right after finishing watching the lecture but no later than Nov. 17, 2020, 8:00pm


THE NUMBER OF ATTENDANCE QUESTIONS WERE:

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

Question 1
When was Rabi Levi born and die?

Answer 1
Born - 1288
Died - 1344

Question 2
When was ET Bell born and die? What is he famouse for?

Answer 2
Born Feb 7 1883
Died - 1960
Pretty famous for his book Men of Mathematics

Question 3
What is his pen name?

Answer 3
John Taine

Question 4
How many set partiotions of a 300 element set are there with exactly 5 members

Answer 4
652759846354937088556719084676441820841461277955440992947509873566186746926913477804190102993738747288558962817342280333376601229437981981830595329045912585294619756668990529039361421955723871166709352362795052056089329148797166961882653114077768994187647185241827325815215774834594663417856252836646111829015715654359914527131889123171510853566878325686289541262450695986313848237131721332315997927035109376

Question 5
Is 1, 1, 4, 11, 41, 162... in the OEIS?
What is the A number

Answer 5
Yes it is in the OEIS
A000296		Set partitions without singletons: number of partitions of an n-set into blocks of size > 1. Also number of cyclically spaced (or feasible) partitions.

Question 6
Let a_k(n) be the number do permutations where every cycle is of length at least k
a_1(n) = n!
a_2(n) = d(n)
for k =3, k=4, k=5, ... find the first 30 term sof a_k(n) and see whether there are already in the OEIS? Which k is the smallest that is not there

Answer 6
k = 3
0, 0, 2, 6, 24, 160, 1140, 8988, 80864, 809856, 8907480, 106877320, 1389428832, 19452141696, 291781655984, 4668504894480, 79364592318720, 1428562679845888, 27142690734936864, 542853814536802656, 11399930109077490560, 250798462399300784640, 5768364635100620089152, 138440751242507472273856, 3461018781064593367693824, 89986488307675206245836800, 2429635184307185219369763200, 68029785160601345467104670848, 1972863769657440129000783404544, 59185913089723198139150966450176
A038205		Number of derangements of n where minimal cycle size is at least 3.

k = 4
0, 0, 1, 6, 24, 130, 930, 7644, 68824, 685656, 7535340, 90457840, 1176171216, 16466275176, 246988107184, 3951794537040, 67180633256640, 1209252349298944, 22975793737934544, 459515836026817056, 9649832432640849280, 212296314644126875680, 4882815247362243598176, 117187565931600216644416, 2929689147731179453981824, 76171917838532634871190400, 2056641781659044077126158400, 57585969886697625971808647424, 1669993126714400894865685465344, 50099793801417192589876087970176


No result for this

k = 4 is not present

Should it be there?

I don't think so. It doesn't really come up in anything. Would be useful in finding the probabilty of the drunk hat problem where 4 pf them get their hat back