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Recent questions tagged generatingfunctions
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1
Generating functions
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
4 days
ago
in
Mathematical Logic
by
shraddha priya
Active
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3.3k
points)

34
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generatingfunctions
discretemathematics
0
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0
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2
SELF DOUBT GENERATING FUNCTION
Difference between getting closed form of generating function and closed form of the given sequence ,pls someone explain with an example
asked
Dec 10
in
Combinatory
by
codingo1234
(
457
points)

18
views
generatingfunctions
recurrence
0
votes
0
answers
3
Kenneth_Rosen_GF
Find a closed form for the exponential generating function for the sequence $\{a_n\}$ where $a_n=\frac{1}{(n+1)(n+2)}$ I broke it down into partial fractions and got $a_n=\frac{1}{n+1}\frac{1}{n+2}$ ... $\sum_{n=0}^{\infty}\frac{1}{(n+2)}.\frac{x^n}{n!}$
asked
Dec 4
in
Combinatory
by
Ayush Upadhyaya
Boss
(
19k
points)

40
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generatingfunctions
0
votes
0
answers
4
Generating function(Find Coefficient of x^100)
asked
Dec 3
in
Combinatory
by
!KARAN
Junior
(
915
points)

61
views
generatingfunctions
discretemathematics
permutationsandcombinations
0
votes
3
answers
5
Generating Function
What will be solution of this function for coefficient of $x^{100}$? $\frac{1}{\left ( 1x^{10} \right )(1x^{20})(1x^{50})}$
asked
Dec 3
in
Combinatory
by
srestha
Veteran
(
104k
points)

140
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generatingfunctions
discretemathematics
0
votes
1
answer
6
GENERATING FUNCTIONS
asked
Oct 26
in
Combinatory
by
Balaji Jegan
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4.3k
points)

87
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generatingfunctions
0
votes
0
answers
7
General Doubt on Generating Functions
Given only a Generating Function in closed form can we find the sequence it represents? If so, how? Please explain with an example.If not, given a GF(closed form) in general what information does it convey to us about a series if the series is not provided ?
asked
Oct 16
in
Combinatory
by
tonystark
(
115
points)

24
views
generatingfunctions
discretemathematics
kennethrosen
permutationsandcombinations
#counting
+1
vote
1
answer
8
Rosen Generating functions
Find a closed form of the generating function of the following sequence $0, 1, 2, 4, 8, 16, 32,64,.....$
asked
Oct 14
in
Combinatory
by
Mk Utkarsh
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(
29.8k
points)

68
views
generatingfunctions
kennethrosen
0
votes
1
answer
9
Find closed form for the generating function
asked
Oct 13
in
Combinatory
by
Mk Utkarsh
Boss
(
29.8k
points)

58
views
generatingfunctions
discretemathematics
kennethrosen
+1
vote
1
answer
10
Self doubt #Generating functions
$\sum_{.}^{.} (3r^{2} + 5r 21) x^{r}$will be equal to :?
asked
Oct 8
in
Combinatory
by
Priyanka17
Active
(
1.1k
points)

48
views
generatingfunctions
+1
vote
1
answer
11
Kenneth Rosenex 6.4_6
Find the closed form for the generating function for the sequence $\{a_n\}$ where (a)$a_n=\binom{n}{2}$ for $n=0,1,2....$ (b)$a_n=\binom{10}{n+1}$ for $n=0,1,2....$
asked
Sep 27
in
Combinatory
by
Ayush Upadhyaya
Boss
(
19k
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70
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kennethrosen
generatingfunctions
discretemathematics
0
votes
1
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12
Generating function
Find the coefficient of x^9 in the power series of each of these functions. a) (x3+x5+x6).(x3+x4).(x+x2+x3+x4+⋯) b) (1+x+x^2)^3
asked
Sep 26
in
Combinatory
by
Na462
Loyal
(
7.5k
points)

87
views
generatingfunctions
discretemathematics
kennethrosen
permutationsandcombinations
+2
votes
2
answers
13
Generating function
Please tell me the approach of solving the question for finding a closed formula for the given generating function: $x^{2} / (1x)^{2}$ . Please determine the general approach how to solve
asked
Sep 25
in
Combinatory
by
Na462
Loyal
(
7.5k
points)

100
views
generatingfunctions
discretemathematics
kennethrosen
0
votes
2
answers
14
Rolling of a dice
The number of ways to roll 5 six sided dice to get sum of 25 is ________. _________________________________________________________ if solving with generating function, then why dividing by $\left ( 1x \right )$ if equation is $\frac{x\left ( 1x^{6} \right )}{\left ( 1x \right )}$?
asked
Aug 23
in
Combinatory
by
srestha
Veteran
(
104k
points)

104
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generatingfunctions
+1
vote
1
answer
15
Rosen book Generating Functions pg no 430
asked
Aug 15
in
Combinatory
by
anip
(
33
points)

67
views
kennethrosen
generatingfunctions
discretemathematics
#counting
+1
vote
0
answers
16
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)

117
views
generatingfunctions
preparation
0
votes
1
answer
17
Combinatorics kenneth Rosen(ex 6.4 47e)
asked
Jun 26
in
Combinatory
by
Ayush Upadhyaya
Boss
(
19k
points)

128
views
kennethrosen
generatingfunctions
discretemathematics
0
votes
1
answer
18
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
(
19k
points)

105
views
discretemathematics
generatingfunctions
kennethrosen
0
votes
0
answers
19
Combinatorics  Kenneth Rosen(Ex 6.4 7c)
asked
Jun 25
in
Combinatory
by
Ayush Upadhyaya
Boss
(
19k
points)

64
views
kennethrosen
generatingfunctions
discretemathematics
+1
vote
1
answer
20
generating funtion
1/1−2x2 provide close formula for the sequences it determines
asked
Jun 14
in
Combinatory
by
sunil sarode
Active
(
1.4k
points)

59
views
generatingfunctions
kennethrosen
discretemathematics
0
votes
1
answer
21
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 $X_{1}+X_{2}+.......X_{7}=11$ $(x+x^{2}+x^{3})^{7}$ $(x(1+x+x^{2}))^{7}$ $x^{7}(1+x+x^{2})^{7}$ ... (7k) (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
(
275
points)

75
views
engineeringmathematics
generatingfunctions
discretemathematics
counting
+2
votes
4
answers
22
kennneth rosen chapter counting
1. Find the coefficient of $x^{10}$ in the power series. $\left ( 1+x^{2}+x^{4}+x^{6}+x^{8}+.... \right )\left ( 1+x^{4}+x^{8}+x^{12}+.... \right )\left ( 1+x^{6}+x^{12}+x^{18}+.... \right )$ ... ........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
(
275
points)

197
views
generatingfunctions
+1
vote
2
answers
23
Generating Function
Find $\left [ x^{50} \right ]$ $\left ( x^{6}+x^{7}+x^{8}+.... \right )^{6}$
asked
May 18
in
Combinatory
by
Nils
Junior
(
907
points)

124
views
generatingfunctions
+1
vote
1
answer
24
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
(
275
points)

74
views
engineeringmathematics
generatingfunctions
0
votes
0
answers
25
Exponential Generating Function
Is Exponential Generating Functions asked in GATE ?
asked
Apr 30
in
Mathematical Logic
by
Na462
Loyal
(
7.5k
points)

36
views
generatingfunctions
+1
vote
1
answer
26
Kenneth Rosen, Generating Functions, Exercise  6.4 QNO33
asked
Apr 12
in
Combinatory
by
Abhinavg
(
419
points)

176
views
kennethrosen
discretemathematics
generatingfunctions
0
votes
1
answer
27
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
Loyal
(
7.5k
points)

126
views
discretemathematics
generatingfunctions
kennethrosen
permutationsandcombinations
+2
votes
2
answers
28
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)

151
views
generatingfunctions
discretemathematics
+1
vote
1
answer
29
Generating function doubt
Please give me clarification
asked
Feb 24
in
Combinatory
by
Lakshman Patel RJIT
Boss
(
20.8k
points)

257
views
discretemathematics
generatingfunctions
+2
votes
0
answers
30
Extended Binomial Coefficients
Find the value of extended Binomial Coefficient $\binom{1/2}{3}$
asked
Feb 24
in
Combinatory
by
Mk Utkarsh
Boss
(
29.8k
points)

102
views
permutationsandcombinations
generatingfunctions
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