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Question 1

0votes

0answers

19views

Is it valid to compare solving vs checking NP problems using average time per logical step?

I’ve been exploring a measurement approach for NP and NP-complete problems based on average time per logical step.I define:...

Israeli Ochimnai

1

asked5 hours ago

Question 2

0votes

1answer

102views

Solutions to $x^n \equiv x \pmod{n}$ for composite $n$.

By Fermat's Little Theorem we know that if $p$ is some prime number, the congruence $x^p \equiv x \pmod{p}$ is solved by any integer $x$, but can we say something about the solutions to $x^n \equiv x \...

Robert Lee

7,746

askedyesterday

Question 3

-1votes

0answers

35views

Proof of Linearly independece set [duplicate]

Let $L_S:F^n→F^m$ be a linear map which has null space $O$.Prove: if $H^1,\dots,H^k$ are linearly independent elements in $F^n$, then $L_S (H^1 ),\dots,L_S (H^k )$ are linearly independent elements ...

William Avila Aguilar

39

askedNov 24 at 16:08

Question 4

3votes

0answers

97views

Integer sequence with largest prime factor

Consider the function $F:\mathbb{N}\to\mathbb{N}$ such that $F(n)=\tfrac{n^2-n}{\delta(n^2-n)}$, where $\delta$ returns the biggest prime factor of its input. I wonder if this function always ...

Cristian Baeza

965

askedNov 24 at 0:14

Question 5

5votes

1answer

181views

Arrangements of 10 Balls Chosen from Red and Blue, Where Every Blue Ball Has a Blue Neighbor(need pure combinatorics solution)

QuestionConsider a linear arrangement of $10$ balls selected from an infinite supply of blue and red balls.Determine the total number of distinct arrangements that satisfy the following condition:...

thedeepdeepsky

439

askedNov 22 at 13:27

Question 6

0votes

1answer

87views

How many odd numbers are there in one row in Pascal's triangle?

I was looking at the pattern of odd entries in Pascal’s triangle and noticed that every row contains an even count of odd numbers. This is easy to justify, but it led me to wonder how the exact count ...

pie

9,247

askedNov 21 at 23:19

Question 7

0votes

0answers

32views

The Homotopy and Homology type of Hyperplane arrangements

This is a theorem in "Homotopy Types of Subspace Arrangementsvia Diagrams of Spaces" by Ziegler and Zivaljevic. I would be interested in if we can say more in the Case where $\mathcal{A}$ ...

user1072285

885

askedNov 20 at 19:25

Question 8

-2votes

0answers

32views

A problem concerning graph probelm in discrete structure [closed]

Prove by induction that in a simple graph, from any vertex that has odd degree, there is a path to another vertex with odd degree.

Ethen

1

askedNov 20 at 5:40

Question 9

3votes

3answers

341views

How many ways to arrange BOOKKEEPER where two E’s appear consecutively but not three.

Q: How many ways to arrange BOOKKEEPER where two E’s appear consecutively but not three.Here What I've got : a) We can consider the two consecutive E’s as one block say X. Hence, we get a new string: ...

Jonathan

33

askedNov 19 at 0:17

Question 10

12votes

5answers

543views

Non-recursive, explicit rational sequence that converges to $\sqrt{2}$

Is there a non-recursive, explicit sequence of rational numbers that has $\sqrt{2}$ as a limit?I know of rational sequences such as $x_{n+1}=(x_n+2/x_{n})/2$ and $q_n=[10^n\sqrt{2}]/10^n$ that have $\...

Francesco Bollini

155

askedNov 18 at 17:55

Question 11

1vote

0answers

38views

VC exponent of a set system

I would like to prove that the VC dimension of a set system $(X,\mathcal{R})$ never takes values in $(0,1).$For the sake of completeness, I'll define some basic ideas in this context.Definition: A ...

giorgioh

354

askedNov 17 at 22:19

Question 12

-1votes

1answer

53views

Justification for Definition of Directed and Undirected Graph

It is commonly known that directed graphs are defined as a double $G_d:=(V,E)$ such that $E \subseteq V^2$, and that undirected graphs $G_u:=(V,E)$ such that $E \subseteq \left\{ \{a,b\}\Big\vert a \...

Ultrio

71

askedNov 17 at 7:39

Question 13

-1votes

1answer

100views

Counting permutations where each element is the maximum or minimum of the prefix [duplicate]

I am trying to solve a combinatorial problem regarding a specific class of permutations.The Problem:Consider a permutation $\sigma$ of the set $\{1, 2, \dots, n\}$, where $n=13$.The permutation ...

thedeepdeepsky

439

askedNov 16 at 8:38

Question 14

0votes

1answer

114views

Defining ordinal multiplication for infinite families of ordinals without transfinite recursion

In Naive Set Theory p.82-83, Halmos defines ordinal addition by defining the ordinal sum of an infinite family ${A_i}$ of well-ordered sets, indexed by some well ordered set $I$. He then proceeds to ...

Or Gold

23

askedNov 15 at 22:05

Question 15

6votes

1answer

140views

Finding $\lim_{n \to \infty} \frac{l(n)}{n^2}$ for minimal vertex coloring satisfying a property for all $k \times k$ sub-squares

I am working on the following grid coloring problem and am stuck on finding the general form of $l(n)$.The ProblemSome of the vertices of the unit squares of an $n \times n$ chessboard are colored ...

匚ㄖㄥᗪ乇ᗪ

963

askedNov 15 at 16:30

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Stack Exchange Network

Questions tagged [discrete-mathematics]

Is it valid to compare solving vs checking NP problems using average time per logical step?

Solutions to $x^n \equiv x \pmod{n}$ for composite $n$.

Proof of Linearly independece set [duplicate]

Integer sequence with largest prime factor

Arrangements of 10 Balls Chosen from Red and Blue, Where Every Blue Ball Has a Blue Neighbor(need pure combinatorics solution)

How many odd numbers are there in one row in Pascal's triangle?

The Homotopy and Homology type of Hyperplane arrangements

A problem concerning graph probelm in discrete structure [closed]

How many ways to arrange BOOKKEEPER where two E’s appear consecutively but not three.

Non-recursive, explicit rational sequence that converges to $\sqrt{2}$

VC exponent of a set system

Justification for Definition of Directed and Undirected Graph

Counting permutations where each element is the maximum or minimum of the prefix [duplicate]

Defining ordinal multiplication for infinite families of ordinals without transfinite recursion

Finding $\lim_{n \to \infty} \frac{l(n)}{n^2}$ for minimal vertex coloring satisfying a property for all $k \times k$ sub-squares

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