User Bach

5

votes

3

answers

167

views

Exercise 6.11 from Isaac's Character theory of finite groups.

Nov 13 '19 at 13:57 Beginner 9,570

2

votes

1

answer

46

views

How many binary strings of length $n$ contain $k$ flips?

combinatorics

Sep 22 '19 at 18:40 Bach 4,745

2

votes

1

answer

174

views

Understanding the difference between the multinomial coefficients and the Stirling number of the 2nd kind

combinatorics

Sep 13 '19 at 0:22 Donald Splutterwit 34.4k

3

votes

1

answer

184

views

Finding the Jordan canonical form when the characteristic polynomial does not split?

linear-algebra jordan-normal-form

Sep 7 '19 at 1:03 Luca Morstabilini 101

5

votes

2

answers

416

views

Prove that $C_0(X)$ is separable given that X is locally compact metric space

functional-analysis banach-spaces separable-spaces function-spaces

Sep 7 '19 at 2:34 Nate Eldredge 82.5k

5

votes

1

answer

229

views

$f(z)=z^n+a_{n-1}z^{n-1}+\cdots+ a_0\in\mathbb Z[z]$ has all its roots on the unit circle. Prove that any root of $f(z)=0$ is a root of unity.

complex-analysis number-theory polynomials

Aug 14 '19 at 17:11 Mindlack 19.8k

5

votes

1

answer

191

views

Sequence that converges in $L^{2}$ on the real line but nowhere pointwise

real-analysis convergence-divergence pointwise-convergence

Oct 1 at 7:33 daw 35.6k

1

vote

1

answer

166

views

Let group $G$ acts transitively on finite sets $\Omega$ and $\Psi$, with $1<|\Omega|<|\Psi|$. If $G$ is simple, show that $|\Psi|$ cannot be prime.

abstract-algebra group-theory group-actions

Aug 13 '19 at 14:31 John Doe 336

3

votes

1

answer

614

views

Graph with $2n$ vertices and $n^2+1$ edges has at least $n$ triangles.

combinatorics graph-theory extremal-combinatorics extremal-graph-theory

Jul 16 at 20:46 Don Thousand 11.4k

2

votes

1

answer

111

views

Extension of map $f$

general-topology

Aug 6 '19 at 13:37 Paul Frost 40.7k

3

votes

1

answer

126

views

Finding a necessary and sufficient condition for a free abelian group of rank $1$

abstract-algebra group-theory modules

Aug 11 '19 at 17:45 Community♦ 1

3

votes

1

answer

447

views

How do I prove that $x^n+x^{n-1}+…+x^2-nx+1=0$ ($n>2$) has one and only one root in $(0,1)$

polynomials roots recreational-mathematics

Dec 10 '19 at 19:48 Vendetta 965

2

votes

3

answers

135

views

$3\times 3$ real orthogonal matrix $A$ with characteristic polynomial $(x+1)(x-1)^2$ is symmetric

linear-algebra orthogonal-matrices

Aug 2 '19 at 8:42 user1551 108k

1

vote

2

answers

166

views

Analytic function from $\mathbb D$ to $\mathbb D$ that preserves the boundary is a rational function

complex-analysis

Jul 30 '19 at 8:47 José Carlos Santos 320k

11

votes

1

answer

256

views

Over which fields (besides $\mathbb{R}$) is every symmetric matrix potentially diagonalizable?

linear-algebra abstract-algebra finite-fields diagonalization symmetric-matrices

Jul 29 '19 at 18:00 Eric Wofsey 263k

3

votes

1

answer

132

views

Matrices commuting with a given $3\times 3$ complex matrix.

linear-algebra abstract-algebra matrices

Jul 25 '19 at 14:09 Magma 4,645

7

votes

1

answer

187

views

A question about groups of order $504=2^3\cdot 3^2 \cdot 7$

abstract-algebra group-theory finite-groups sylow-theory

Jul 24 '19 at 9:41 Bach 4,745

0

votes

2

answers

140

views

Entire function, periodic on real line implies periodic on $\mathbb{C}$?

complex-analysis periodic-functions entire-functions

Jul 24 '19 at 5:44 Chris Custer 40.1k

2

votes

3

answers

134

views

Looking for a Simple Proof of the Divergence of the Prime Harmonic Series

sequences-and-series elementary-number-theory prime-numbers

Jul 27 '19 at 5:23 SARTHAK GUPTA 1,168

2

votes

1

answer

118

views

Let $p(z)=z^n+a_{n-1}z^{n-1}+a_{n-2}z^{n-2}+…+a_0$ be a complex polynomial satisfying $|p(z)| \leq 1$ for $|z|\leq 1$, then prove that $p(z)=z^n$ [duplicate]

complex-analysis analytic-functions

Jul 23 '19 at 7:24 Kavi Rama Murthy 249k

0

votes

1

answer

42

views

A question on the homogeneous subspaces on the unit circle

real-analysis fourier-analysis fourier-series harmonic-analysis

May 15 at 19:54 Bach 4,745

7

votes

1

answer

205

views

Differentiability of $ G(x)=\int_{\mathbb R} e^{tx}f(t)dt $ on $ (0,1) $

real-analysis derivatives

Jul 23 '19 at 11:05 Community♦ 1

3

votes

1

answer

120

views

Non-negative integrable functions converging in measure on $[0,1]$ with $ \lim_{k\to\infty}\int_0^1 f_k(x)dx=\int_0^1 f(x)dx .$

real-analysis measure-theory lebesgue-integral

Jul 18 '19 at 4:28 Bach 4,745

2

votes

1

answer

47

views

On inverse matrices of linear combination of permutation matrices

linear-algebra matrices

Jul 13 '19 at 17:30 user1551 108k

10

votes

2

answers

575

views

$A$ and $A^2$ have same characteristic polynomial

linear-algebra matrices complex-numbers diagonalization characteristic-functions

Jul 13 '19 at 4:19 Martin Sleziak 51.9k

11

votes

1

answer

428

views

If $|G|=36$ then $G$ has either a normal $2$-Sylow or a normal $3$-Sylow

abstract-algebra group-theory finite-groups sylow-theory

Jul 13 '19 at 21:04 Jyrki Lahtonen 119k

1

vote

2

answers

273

views

On entire functions of finite order

complex-analysis entire-functions

Jul 12 '19 at 10:05 reuns 53k

2

votes

1

answer

153

views

Let $f$ be a Lebesgue integrable function on $\mathbb R$. Prove that $ \lim_{n\to\infty}\int_{-\infty}^\infty (\cos x)^nf(x)dx=0 $

real-analysis integration limits

Jul 5 '19 at 13:50 J.A.G 719

4

votes

3

answers

92

views

Show that a function satisfies $|f(z)|<1$ for all $z$ in the open left half plane.

complex-analysis complex-numbers

Jul 5 '19 at 5:35 Sangchul Lee 127k

6

votes

6

answers

152

views

Find closed formula without using induction for $\sum_{k=0}^n k^3$

discrete-mathematics generating-functions closed-form

Jun 28 '19 at 0:28 J. W. Tanner 54.5k

Stack Exchange Network

current community

your communities

more stack exchange communities

Next privilege

Next badge

1,699 Bookmarks

Exercise 6.11 from Isaac's Character theory of finite groups.

How many binary strings of length $n$ contain $k$ flips?

Understanding the difference between the multinomial coefficients and the Stirling number of the 2nd kind

Finding the Jordan canonical form when the characteristic polynomial does not split?

Prove that $C_0(X)$ is separable given that X is locally compact metric space

$f(z)=z^n+a_{n-1}z^{n-1}+\cdots+ a_0\in\mathbb Z[z]$ has all its roots on the unit circle. Prove that any root of $f(z)=0$ is a root of unity.

Sequence that converges in $L^{2}$ on the real line but nowhere pointwise

Let group $G$ acts transitively on finite sets $\Omega$ and $\Psi$, with $1<|\Omega|<|\Psi|$. If $G$ is simple, show that $|\Psi|$ cannot be prime.

Graph with $2n$ vertices and $n^2+1$ edges has at least $n$ triangles.

Extension of map $f$

Finding a necessary and sufficient condition for a free abelian group of rank $1$

How do I prove that $x^n+x^{n-1}+…+x^2-nx+1=0$ ($n>2$) has one and only one root in $(0,1)$

$3\times 3$ real orthogonal matrix $A$ with characteristic polynomial $(x+1)(x-1)^2$ is symmetric

Analytic function from $\mathbb D$ to $\mathbb D$ that preserves the boundary is a rational function

Over which fields (besides $\mathbb{R}$) is every symmetric matrix potentially diagonalizable?

Matrices commuting with a given $3\times 3$ complex matrix.

A question about groups of order $504=2^3\cdot 3^2 \cdot 7$

Entire function, periodic on real line implies periodic on $\mathbb{C}$?

Looking for a Simple Proof of the Divergence of the Prime Harmonic Series

Let $p(z)=z^n+a_{n-1}z^{n-1}+a_{n-2}z^{n-2}+…+a_0$ be a complex polynomial satisfying $|p(z)| \leq 1$ for $|z|\leq 1$, then prove that $p(z)=z^n$ [duplicate]

A question on the homogeneous subspaces on the unit circle

Differentiability of $ G(x)=\int_{\mathbb R} e^{tx}f(t)dt $ on $ (0,1) $

Non-negative integrable functions converging in measure on $[0,1]$ with $ \lim_{k\to\infty}\int_0^1 f_k(x)dx=\int_0^1 f(x)dx .$

On inverse matrices of linear combination of permutation matrices

$A$ and $A^2$ have same characteristic polynomial

If $|G|=36$ then $G$ has either a normal $2$-Sylow or a normal $3$-Sylow

On entire functions of finite order

Let $f$ be a Lebesgue integrable function on $\mathbb R$. Prove that $ \lim_{n\to\infty}\int_{-\infty}^\infty (\cos x)^nf(x)dx=0 $

Show that a function satisfies $|f(z)|<1$ for all $z$ in the open left half plane.

Find closed formula without using induction for $\sum_{k=0}^n k^3$