1
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1answer
53 views

Prove a polynomial in Fq is a permutation polynomial of Fqn with a necessary and sufficient condition

P.S This is the best Math Expression I can edit. I am real shameful, where can I find the introduction of typing in this webset? thank you Exercise7.13 Let\[f\left( x \right) = \sum\limits_{i = ...
2
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1answer
40 views

How to convert a permutation to permutation polynomial?

Let Fq be the finite field with q elements, where q is a prime power. A permutation on Fq is a bijection from Fq to itself. Let Fq[x] be the ring of polynomials in a single indeterminate x over Fq. A ...
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1answer
55 views

Can this polynomial transformation produce new symmetry?

I've got a polynomial transformation on $\mathbb{R}^6$, and I have a conjecture about it, but I'm having a hard time proving it. The transformation looks like this: $ u:= abcde + abc + abe + ade + ...
2
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0answers
167 views

Getting K heads out of N biased coins problem (formula generation ).

Problem- Given a set of coins n with each coin i having Pi probability to give heads. Find the probability of getting k heads, when all coins are tossed together. hi i have solved this problem ...
2
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1answer
60 views

Any comprehensive material to revise the mathematics

I left school long back and so my mathematics knowledge also fades out. I am trying hard to re-collect the basics about log / permutaion / combination / probability / polynomial equations. I tried ...
3
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1answer
119 views

Polynomials and partitions

There is a question I have based on the fact: If you take a quadratic polynomial with integer coefficients, and take the set (1,2,3,4,5,6,7,8), and make a partition A=(1,4,6,7), and B=(2,3,5,8), and ...
13
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3answers
300 views

How to see that the polynomial $4x^2 - 3x^7$ is a permutation of the elements of $\mathbb{Z}/{11}\mathbb{Z}$

This is from Rotman's Group Theory book, although I don't have the specific reference right now, as the book is with a friend. He asks to show that $\alpha (x) = 4x^2 - 3x^7$ is a permutation of the ...
6
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2answers
280 views

Number of terms in a monomial symmetric polynomial

Is there a closed form expression for the number of terms in a monomial symmetric polynomial in a given number of variables for a particular partition of exponents, in terms of which/how many ...