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Recent questions tagged generatingfunctions
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ISI2018MMA26
Let $C_i(i=0,1,2...n)$ be the coefficient of $x^i$ in $(1+x)^n$.Then $\frac{C_0}{2} – \frac{C_1}{3}+\frac{C_2}{4}\dots +(1)^n \frac{C_n}{n+2}$ is equal to $\frac{1}{n+1}\\$ $\frac{1}{n+2}\\$ $\frac{1}{n(n+1)}\\$ $\frac{1}{(n+1)(n+2)}$
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ACE Test Series: Generating Function
The generating function of the sequence $\left \{ a_{0},a_{1},a_{2}..........a_{n}………...\infty \right \}$ where $a_{n}=\left ( n+2 \right )\left ( n+1 \right ).3^{n}$ is $a)3\left ( 1+3x \right )^{2}$ $b)3\left ( 13x \right )^{2}$ $c)2\left ( 1+3x \right )^{3}$ $d)2\left ( 13x \right )^{3}$
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Rosen 7e, Advance Counting techniques , Question 6.f
Find the generating function for the sequence $\left \{ a_n \right \} where $ $a_n = \Large \binom{10}{n+1} $ ... $\Large \color{red}{ \frac{( 1+x )^{10}  1}{x} }$ Please verify
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generating function
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Jan 15
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MadeEasy Full Length Test 2019: Combinatory  Generating Functions
Let We define Then ar is equal to. $\binom{r}{2019}$ $\binom{r}{r + 2018}$ $\binom{r}{2019  r}$ $\binom{r}{r  2018}$ Can anyone tell me if this type of question is in Gate 2019 syllabus or ... question in previous year question? If yes, then when can I learn this stuff from. Because I am unable to understand the whole solution.
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madeeasytestseries
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Kenneth Rosen Edition 6th Exercise 7.4 Question 7,8 (Page No. 496)
For each of these generating functions, provide a closed formula for the sequence it determines. $a) (3x − 4)^{3}$ $b) (x^{3} + 1)^{3}$
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Dec 29, 2018
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Sandy Sharma
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7
MadeEasy Test Series 2019: Combinatory Generating Functions
Let $M(x) = \frac{x^{2018}}{(1x)^{2019}}$ we define $M(x) = \sum_{r=0}^{\infty}a_{r}x^{r}$ ,then $a_{r}$ is equal to $A)\binom{r}{2019}$ $B)\binom{r}{r+2018}$ $C)\binom{r}{2019r}$ $D)\binom{r}{r2018}$
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Dec 15, 2018
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register_user_19
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madeeasytestseries2019
madeeasytestseries
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8
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 __________ .
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Dec 12, 2018
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shraddha priya
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9
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, 2018
in
Combinatory
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codingo1234
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791
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41
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generatingfunctions
recurrence
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10
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 $a_n=\frac{1}{n+1}\frac{1}{n+2}$ ... $\sum_{n=0}^{\infty}\frac{1}{(n+2)}.\frac{x^n}{n!}$
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Dec 4, 2018
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Combinatory
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Ayush Upadhyaya
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11
Kenneth Rosen Edition 6th Exercise 6.4 Question 13 (Page No. 440)
Use Generating function to determine,the number of different ways $10$ identical balloons can be given to four children if each child receives atleast $2$ ballons? Ans given $(x^{2}+x^{3}+.........................)^{4}$ But as there is a upper ... Which one is correct? plz confirm
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Dec 4, 2018
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Combinatory
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srestha
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12
Generating function(Find Coefficient of x^100)
How to find coefficient of $x^{100}$? $ = (1+x^{10}+(x^{10})^2 + \dots)(1+x^{20}+(x^{20})^2 + \dots)(1+x^{50}+(x^{50})^2 + \dots)\\ = (\frac{1}{1x^{10}}).(\frac{1}{1x^{20}}).(\frac{1}{1x^{50}}) $
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Dec 3, 2018
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!KARAN
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3
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13
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, 2018
in
Combinatory
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srestha
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14
GENERATING FUNCTIONS
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Oct 26, 2018
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Balaji Jegan
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15
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 ?
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Oct 16, 2018
in
Combinatory
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tonystark
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173
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44
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kennethrosen
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#counting
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1
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16
Kenneth Rosen Edition 6th Exercise 7.4 Question 4g (Page No. 496)
Find a closed form of the generating function of the following sequence $0, 1, 2, 4, 8, 16, 32,64,.....$
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Oct 14, 2018
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Combinatory
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Mk Utkarsh
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17
Kenneth Rosen Edition 6th Exercise 7.4 Question 3e (Page No. 496)
Find closed form for the generating function of the following sequence $\binom{7}{0}, \binom{7}{1}, \binom{7}{2}, ......., \binom{7}{7},0,0,0,0,0,...$
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Oct 13, 2018
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Combinatory
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Mk Utkarsh
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kennethrosen
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18
Self doubt #Generating functions
$\sum_{.}^{.} (3r^{2} + 5r 21) x^{r}$will be equal to :?
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Oct 8, 2018
in
Combinatory
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Priyanka17
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19
Kenneth Rosen Edition 6th Exercise 7.4 Question 6 (Page No. 496)
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 $n=0,1,2....$
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Sep 27, 2018
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Combinatory
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Ayush Upadhyaya
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20
Kenneth Rosen Edition 6th Exercise 6.4 Question 10 (Page No. 440)
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
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Sep 26, 2018
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Combinatory
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Na462
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2
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21
Kenneth Rosen Edition 6th Exercise 6.4 Question 7g (Page No. 440)
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
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Sep 25, 2018
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Combinatory
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Na462
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kennethrosen
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2
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22
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 $\frac{x\left ( 1x^{6} \right )}{\left ( 1x \right )}$?
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Aug 23, 2018
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Combinatory
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srestha
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23
Kenneth Rosen Edition 6th Exercise 6.4 Example 15 (Page No. 435 )
How to find the coefficient ( for eg $x^7$ ) in the generating function$(1+x+x^2+x^3+..)(1+x^2+x^4+x^6+..)(1+x^5+x^{10}+x^{15}+..)$ ?
asked
Aug 15, 2018
in
Combinatory
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anip
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23
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95
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kennethrosen
generatingfunctions
discretemathematics
#counting
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0
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24
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
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Jul 19, 2018
in
Combinatory
by
Tridhara Chakrabarti
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349
points)

276
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generatingfunctions
preparation
0
votes
1
answer
25
Kenneth Rosen Edition 6th Exercise 6.4 Question 47 e (Page No. 443)
Find the sequence with each of these functions as its exponential generating function g(x) = $e^{2x}  \frac{1}{1x}$ ... , according to rosen's answer $a_0$ should exist but in my answer $a_0$ is 0. Please let me know where I am missing something.
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Jun 26, 2018
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Combinatory
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Ayush Upadhyaya
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26
Kenneth Rosen Edition 6th Exercise 6.4 Question 46 e (Page No. 443)
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 $\sum_{n=0}^{\infty}\frac{a_n}{n!}x^n$
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Jun 26, 2018
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Combinatory
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Ayush Upadhyaya
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kennethrosen
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27
Kenneth Rosen Edition 6th Exercise 6.4 Question 8 c (Page No. 440)
1/1−2x2 provide close formula for the sequences it determines
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Jun 14, 2018
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Combinatory
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sunil sarode
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1
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28
Kenneth Rosen Edition 6th Exercise 6.4 Question 6 e (Page No. 440)
nC2 for n=0,1,2,3...
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Jun 14, 2018
in
Mathematical Logic
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sunil sarode
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0
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29
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.
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May 23, 2018
in
Combinatory
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mbisht
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253
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4
answers
30
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, 2018
in
Combinatory
by
mbisht
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253
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215
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generatingfunctions
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