# characters

1. ### Extra Characters?

Hi! This bit of LaTeX gives me two curly brackets and a dollar sign that I didn't intend to put in. I don't know how to get rid of them. Can anybody help? \{\tau _1}{\text{ consists of }}\{\mathbb{R}}{\text{, }}\emptyset {\text{ and every interval }}\left( {a,b} \right){\text{ for }}a{\text{...
2. ### Dirichlet characters

Hi! So i have made a table of all the nonprincipal Dirichlet characters mod 16. Is the following table correct? n 1 3 5 7 9 11 13 15 X1(n) 1 1 1 1 1 1 1 1 X2(n) 1 i -i -1 -1 -i i 1 X3(n) 1 -1 -1 1 1 -1 -1 1 X4(n) 1 -i i -1 -1 i -i 1 X5(n) 1 1 -1 -1 1 1 -1 -1 X6(n) 1 i i 1 -1 -i -i...
3. ### Dirichlet characters

Hi all, sorry if this is in the wrong section....?? I am looking to construct a table of values for all the nonprincipal Dirichlet characters mod 16. Can anyone help? Lexi
4. ### Primitive Characters

Let \chi be the primitive character modulo 12. I need to find all possible values of \underset{m\leq x}{\sum}\chi(m) for varying x (not necessarily an integer). I have an answer which shows that the sum is equal to either 1, 2 or 0, but am not entirely sure it is correct. Could anybody...
5. ### Dirichlet characters

I've been trying to justify the following step in a textbook (Iwaniec-Kowalski) proof, but just can't seem to: \displaystyle \sum_{n\:\equiv\: 0 \mod k} \chi (n) = \sum_{l|k} \mu (l) \sum_{(n,l)=1} \chi (n) where \mu is the Mobius function. It's clearly some application of Mobius inversion...
6. ### Characters on homology groups of simplicial complexes

Hi all, nice to be here I,ve been given this problem and have made some progress with it but am still slightly confused over the statement of it: Essentially I need to find a simplicial complex (Simplicial complex - Wikipedia, the free encyclopedia) such that the alternating sum of the...
7. ### Probability of finding a sequence of k characters in an n characters long text

Hi everyone, I am writing a code-breaking program, and I'm trying to figure out a decision rule, to teach my program how to recognize real text from gibberish. I ran into the problem of calculating the probability of encountering a k-letters word in a random n-letters long text. For example...
8. ### characters of S_n from A_n

Using Frobenius Reciprocity, derive the character table of S_n from that of A_n when (a) n = 3 (b) n = 4 (c) n = 5
9. ### product of characters

Prove that the product of two characters contains the trivial character if and only if the second is the conjugate of the first, in which case it contains the trivial character exactly once.
10. ### characters of S_5

Write the multiplication for the characters of S_5. That is, write every product of irreducible characters as a sum of irreducible characters (the table will be symmetric).
11. ### vector arrow atop two characters

I'd like to create a symbol for a vector that uses two letters-- one each for its initial and terminal points, such as "PQ" with a vector arrow stretching atop both letters. \vec seems to allow only one symbol; something like \overline{PQ} is similar to what I want, but puts a line, not an arrow...
12. ### Characters: The usual suspects

My group theory text (and other sources) say that the character of a n operator in a representation is the trace of the matrix corresponding to the operator. ie. Given a group operator \Gamma in some representation we have X = Tr( \Gamma ). But My newest text says a function (in a space) ca be...
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### [SOLVED] help: strange characters

Hello, Can you tell me what these 18-characternumbers could mean. It has to do with geocaching. Find for every line the value and add these, this gives you ABC. N52 19.ABC As you can see, the result are the last 3 figures of a coordinate. T001B4U27004129907 G001A1P00450058294...