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Recent questions tagged generatingfunctions
+1
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1
answer
1
Rosen book Generating Functions pg no 430
asked
3 days
ago
in
Combinatory
by
anip
(
33
points)

18
views
kennethrosen
generatingfunctions
discretemathematics
#counting
+1
vote
1
answer
2
Generating Function Where to start?
Hello can anyone suggest good video/book to learn generating functions from?..i tried the nptel lecture..it has some audio lag. and i could not make much out of it..I am well versed in combinatorics but my calculus is weak.. Please suggest some resource that teaches generating functions from scratch
asked
Jul 19
in
Combinatory
by
Tridhara Chakrabarti
(
255
points)

56
views
generatingfunctions
preparation
0
votes
1
answer
3
Combinatorics kenneth Rosen(ex 6.4 47e)
asked
Jun 26
in
Combinatory
by
Ayush Upadhyaya
Boss
(
11k
points)

105
views
kennethrosen
generatingfunctions
discretemathematics
0
votes
1
answer
4
CombinatoricsKenneth Rosen (Ex6.445)
Find a closed form for the exponential generating function for the sequence $\{ a_n \}$ where $a_n=\frac{1}{n+1}$ and the exponential generating function for the sequence $\{a_n\}$ is the series $\sum_{n=0}^{\infty}\frac{a_n}{n!}x^n$
asked
Jun 26
in
Combinatory
by
Ayush Upadhyaya
Boss
(
11k
points)

88
views
discretemathematics
generatingfunctions
kennethrosen
0
votes
0
answers
5
Combinatorics  Kenneth Rosen(Ex 6.4 7c)
asked
Jun 25
in
Combinatory
by
Ayush Upadhyaya
Boss
(
11k
points)

45
views
kennethrosen
generatingfunctions
discretemathematics
+1
vote
1
answer
6
generating funtion
1/1−2x2 provide close formula for the sequences it determines
asked
Jun 14
in
Mathematical Logic
by
sunil sarode
Active
(
1.3k
points)

36
views
generatingfunctions
kennethrosen
discretemathematics
0
votes
1
answer
7
Combinatorics
Find the number of seven digit integers with sum of the digits equal to $11$ and formed by using the digits $1,2$ and $3$ only. Soln $X_{1}+X_{2}+.......X_{7}=11$ $(x+x^{2}+x^{3})^{7}$ $(x(1+x+x^{2}))^{7}$ $x^{7}(1+x+x^{2})^{7}$ $x^{7}(\dfrac{1x^{3}}{1x})^ ... (x)3k) * ((7+k1k) xk) $((\binom{7}{k}) (x)^{3k}) \times (\binom{7+k1}{k} x^{k})$ Now not able to proceed. Kindly help.
asked
May 23
in
Combinatory
by
mbisht
(
223
points)

65
views
engineeringmathematics
generatingfunctions
discretemathematics
counting
+2
votes
4
answers
8
kennneth rosen chapter counting
1. Find the coefficient of $x^{10}$ in the power series. $\left ( 1+x^{2}+x^{4}+x^{6}+x^{8}+.... \right )\left ( 1+x^{4}+x^{8}+x^{12}+.... \right )\left ( 1+x^{6}+x^{12}+x^{18}+.... \right )$ Ans. $\frac{1}{\left ( 1x^ ... \right )\left ( 1x^{6} \right )}$........now not able to proceed. 2.Provide a closed formula for the sequence it determines x2+3x+7+(1/(1x2))
asked
May 18
in
Combinatory
by
mbisht
(
223
points)

167
views
generatingfunctions
+1
vote
2
answers
9
Generating Function
Find $\left [ x^{50} \right ]$ $\left ( x^{6}+x^{7}+x^{8}+.... \right )^{6}$
asked
May 18
in
Combinatory
by
Nils
Junior
(
891
points)

87
views
generatingfunctions
+1
vote
1
answer
10
Generating function
1. Find a closed form for the generating function for the sequence $1,1,0,1,1,1,1,1,1,1,...........$ 2. Find a closed form for the generating function for the sequence $a_n= 2n+3$ for all $n=0,1,2,....$
asked
May 17
in
Combinatory
by
mbisht
(
223
points)

60
views
engineeringmathematics
generatingfunctions
0
votes
0
answers
11
Exponential Generating Function
Is Exponential Generating Functions asked in GATE ?
asked
Apr 30
in
Mathematical Logic
by
Na462
Active
(
4.5k
points)

22
views
generatingfunctions
0
votes
1
answer
12
Kenneth Rosen, Generating Functions, Exercise  6.4 QNO33
asked
Apr 12
in
Combinatory
by
Abhinavg
(
325
points)

142
views
kennethrosen
discretemathematics
generatingfunctions
0
votes
1
answer
13
Generating functions
In generating function i studied from books i didn't understand two things 1. How to apply generating functions for solving recurrence relation 2. Generating functions for solving Permutations Can anybody explain it with an example ?
asked
Apr 10
in
Mathematical Logic
by
Na462
Active
(
4.5k
points)

64
views
discretemathematics
generatingfunctions
kennethrosen
permutationsandcombinations
+2
votes
2
answers
14
Generating functions
What will be the coefficient of x^17 in the expansion of (x+x^2+x^3+x^4+x^5+x^6)^4?
asked
Mar 29
in
Combinatory
by
Mayank Khakharia 1
(
45
points)

133
views
generatingfunctions
discretemathematics
+1
vote
1
answer
15
Generating function doubt
Please give me clarification
asked
Feb 24
in
Combinatory
by
Lakshman Patel RJIT
Loyal
(
8k
points)

252
views
discretemathematics
generatingfunctions
+2
votes
0
answers
16
Extended Binomial Coefficients
Find the value of extended Binomial Coefficient $\binom{1/2}{3}$
asked
Feb 24
in
Combinatory
by
Mk Utkarsh
Boss
(
14k
points)

82
views
permutationsandcombinations
generatingfunctions
+1
vote
1
answer
17
Generating Function
How to apply this theorem to $\frac{x^{3}}{1x}$
asked
Feb 24
in
Set Theory & Algebra
by
Mk Utkarsh
Boss
(
14k
points)

122
views
generatingfunctions
discretemathematics
0
votes
3
answers
18
Self doubt generating function
Equation: $x+y=10$ and we are asked to find out the number of a nonnegative integral solution of this equation.
asked
Feb 23
in
Combinatory
by
Lakshman Patel RJIT
Loyal
(
8k
points)

175
views
generatingfunctions
+8
votes
6
answers
19
GATE20181
Which one of the following is a closed form expression for the generating function of the sequence $\{a_n\}$, where $a_n = 2n +3 \text{ for all } n=0, 1, 2, \dots$? $\frac{3}{(1x)^2}$ $\frac{3x}{(1x)^2}$ $\frac{2x}{(1x)^2}$ $\frac{3x}{(1x)^2}$
asked
Feb 14
in
Combinatory
by
gatecse
Boss
(
18.1k
points)

2.5k
views
gate2018
generatingfunctions
normal
+1
vote
0
answers
20
permutations
Let we have 20 identical object and we want to distribute to 6 different person , how many ways are there that each person get atleast one object ? solution : x1 + x2 + x3 +x4 + x5 + x6 = 20 where 1 $\leq x _{i} \leq 20$ we have to find coefficient of $x^{20}$ in $( x ... 1$\times (_{14}^{6+141}\textrm{C} ) = _{14}^{19}\textrm{C}$ $x^{14}$ = 11628 Answer given = 230229 where iam wrong
asked
Jan 25
in
Mathematical Logic
by
sumit goyal 1
Boss
(
12.1k
points)

28
views
discretemathematics
generatingfunctions
permutationsandcombinations
+2
votes
1
answer
21
solve
In how many ways can we distribute 77 apples and 66 oranges among 44 children so that each child gets at least one apple? solve by generating function along with approach thanks
asked
Jan 22
in
Mathematical Logic
by
sumit goyal 1
Boss
(
12.1k
points)

95
views
generatingfunctions
discretemathematics
+1
vote
0
answers
22
solve
There are 4 oranges, 5 apples and 6 mangoes in a basket. In how many ways can a person make a selection when select at least one fruit from each kind? provide approach thanks in advance
asked
Jan 22
in
Mathematical Logic
by
sumit goyal 1
Boss
(
12.1k
points)

43
views
discretemathematics
generatingfunctions
permutationsandcombinations
+3
votes
1
answer
23
solve by generating function along with approach thanks advance
asked
Jan 22
in
Mathematical Logic
by
sumit goyal 1
Boss
(
12.1k
points)

141
views
discretemathematics
generatingfunctions
+4
votes
2
answers
24
How to find the number of solutions value of (n,p) to satisfy (5*n + 9*p) = 23
asked
Jan 16
in
Combinatory
by
hem chandra joshi
Active
(
4.4k
points)

82
views
generatingfunctions
+1
vote
0
answers
25
made easy mock test
The number of ways can 10 balls be chosen from an urn containing 10 identical green balls, 5 identical yellow balls, and 3 identical blue balls are __________.
asked
Jan 13
in
Combinatory
by
mohit kumar 5
Junior
(
605
points)

83
views
permutationsandcombinations
generatingfunctions
madeeasytestseries
+1
vote
0
answers
26
Kenneth Rosen Ex 5.5
How many positive integers less than 1,000,000 have the sum of their digits equal to 19?
asked
Dec 21, 2017
in
Combinatory
by
Ayush Upadhyaya
Boss
(
11k
points)

83
views
generatingfunctions
combinational
0
votes
0
answers
27
Selfdoubt Kenneth Rosen
Can't understand what they did here. How did they find out the value of xG(x)?Example 444. Chapter: Advanced Counting Techniques
asked
Dec 9, 2017
in
Mathematical Logic
by
MrPeppermint
(
465
points)

76
views
generatingfunctions
kennethrosen
+2
votes
1
answer
28
Generating Function
Q.find number of 7 digit number with sum of digits equal to 11 and formed using digits 1 ,2 ,3 Can we do this with help of generating functions.
asked
Nov 25, 2017
in
Combinatory
by
junaid ahmad
Loyal
(
9k
points)

121
views
generatingfunctions
+1
vote
0
answers
29
Self_doubt
How to generalize a given sequence using generating function? If there is a given series say : 1,3,4,5,7,8,10.. how to generalize this sequence? @Habib Sir Please answer this doubt and give a general approach.
asked
Nov 11, 2017
in
Combinatory
by
saxena0612
Boss
(
11.5k
points)

48
views
generatingfunctions
+1
vote
1
answer
30
Kenneth Rosen Ex 6.4
What is the coefficient of x10 in (1+x2+x4+x6+x8+....)(1+x4+x8+x12+....)(1+x6+x12+x18+...) ?
asked
Oct 29, 2017
in
Combinatory
by
Ayush Upadhyaya
Boss
(
11k
points)

136
views
kennethrosen
generatingfunctions
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