Tagged Questions
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1answer
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Find generating function of given problem?
please help me to find the generating function of this problem $a_k = ( k + 1) for k=0,1,2,3,...$
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2answers
45 views
Generating Functions in Discrete Mathematics in Computer Science
Hey Guys can anyone help me with the following question in Discrete Structures in Mathematics, relating generating functions
Find a closed form for the generating function for the sequence $\{a_n\}$, ...
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1answer
24 views
Generating function question
let say I have $90 balls$
$S_{1} = $ green balls
$S_{2} = $ orange balls
$S_{3} = $ red balls
I have the following limitations:
No limit
Choose at most 60 balls from each color
choose even ...
0
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1answer
52 views
How to obtain asymptotic form for sequence, given generating function
Let $a_n$ be the number of ways to obtain the amount of $n$ cents, using a supply of 1-cent coins, 3 types of 2-cent coins, and 4-cent coins. Then, $a_n$ is the coefficient of $x^n$ in ...
1
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1answer
40 views
Generating functions homework question 3
This is a Homework question
Determine the Closed Form generating function for the sequence $a_0,a_1,a_2...,$ where $a_n$ is the number of partitions of the non negative integer n into
a) even ...
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1answer
39 views
Generating Functions Homework Question 2
This is a HW question
The question is to use generating functions to count the number of six digit (positive) integers whose digits sum to $42$. Ex. $978468$ is a six digit integer whose digits sum ...
3
votes
2answers
57 views
generating function Homework Question 1
This is a HW question
I am asked to find a closed form generating function for $1,1,0,1,1,0,1,1,0....$
so then $f(x)=x^0+x^1+0x^2+x^3+x^4+0x^5+x^6+x^7+0x^8$
could use some hint or help.
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2answers
101 views
Recurrence relations and generating functions question
Let $A_n$ be the set of different paving of a $2\times n$ using $2\times 1$ or $1 \times 2$ tiles. We'll define $a_n$=$|A_n|$.
1] Find recurrence relation: I found it -> $a_n=a_{n-1}+a_{n-2}$ with ...
0
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1answer
56 views
A small question about generating functions
just a small question: When should I use infinite geometric sequence and when should I use finite geometric sequence when solving problems involving combinations?
For instance, for the problem: How ...
3
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1answer
66 views
Interpretation of generating function infinite product
Let $P$ denote the set of primes and let $s\in\{-1,1\}$. How can you interpret the coefficient of $x^n$ in the power series expansion of $$\prod_{p\in P} (1+sx^p)^s$$
for either choice of $s$?
I ...
1
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1answer
47 views
Generating functions combinatorical problem
In how many ways can you choose $10$ balls, of a pile of balls containing $10$ identical blue balls, $5$ identical green balls and $5$ identical red balls?
My solution (not sure if correct, would ...
1
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1answer
58 views
Generating function question about arranging n objects with limitations
Generating functions question: There are n objects - rings, earring and bracelets. How many ways are there to arrange these objects, as the amount of earring is even and there are at most 4 bracelets.
...
3
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3answers
86 views
Generating function: Find a closed form of $\sum_{k=0}^n (-3)^k(k+1)$
Find the closed form of $\sum_{k=0}^n (-3)^k(k+1)$.
So the generating function would be: $$A(x)=1-6x+18x^2-108x^3...$$ So what I did notice is that its closed form is perhaps some variation of ...
1
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2answers
80 views
Is my solution correct? Generating functions question: How many non-negative solutions does the equation $x_1+x_2+x_3+x_4+x_5+x_6=12$ have?
so we began studying this subject, and I tried solving this question: How many non-negative and whole ($\in \Bbb Z$) solutions does the equation $x_1+x_2+x_3+x_4+x_5+x_6=12$ have?
I would like to ...
1
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1answer
43 views
Generating functions of partition numbers
I don't understand at all why:
\begin{equation}
\sum\limits_{n=0}^\infty p_n x^n = \prod\limits_{k=1}^\infty (1-x^k)^{-1}
\end{equation}
Where $p_n$ is the number of partitions of $n$. Specifically ...
