Questions tagged [discrete-mathematics]
The study of discrete mathematical structures. Consider using a more specific tag instead, such as: (combinatorics), (graph-theory), (computer-science), (probability), (elementary-set-theory), (induction), (recurrence-relations), etc.
33,607 questions
3 votes
0 answers
72 views
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 ...
- 973
0 votes
1 answer
81 views
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 ...
- 9,065
0 votes
0 answers
74 views
As a high school student, what resources would help me learn the foundation of maths? (axioms and definitions) [closed]
I am a high school sophomore, and I am currently trying to prove everything I have learned about math until now starting from basic axioms and definitions. However, I found it extremely hard to find ...
- 149
0 votes
0 answers
46 views
What are the building blocks of the Integers set? [closed]
Wen looking at the integers set $\mathbb{Z}$, what are its fundamental building blocks? Is it the positive subset $\mathbb{Z}^+$ or is it the negatives $\mathbb{Z}^-$ that form the foundation of the ...
12 votes
5 answers
491 views
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 $\...
-1 votes
1 answer
52 views
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 \...
- 71
-1 votes
1 answer
66 views
Counting permutations where each element is the maximum or minimum of the prefix
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 ...
- 100
6 votes
1 answer
132 views
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 Problem Some of the vertices of the unit squares of an $n \times n$ chessboard are colored ...
- 718