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.
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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)},ドル where $\delta$ returns the biggest prime factor of its input. I wonder if this function always ...
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Arrangements of 10 Balls Chosen from Red and Blue, Where Every Blue Ball Has a Blue Neighbor(need pure combinatorics solution)
Question
Consider a linear arrangement of 10ドル$ balls selected from an infinite supply of blue and red balls.
Determine the total number of distinct arrangements that satisfy the following condition:
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The Homotopy and Homology type of Hyperplane arrangements
This is a theorem in "Homotopy Types of Subspace Arrangements
via Diagrams of Spaces" by Ziegler and Zivaljevic. I would be interested in if we can say more in the Case where $\mathcal{A}$ ...
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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.
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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: ...
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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 ...
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Confusion Matrix word Problem [closed]
Problem #4: Autonomous Vehicle Pedestrian Detection An autonomous vehicle's pedestrian detection system is being tested. Out of 150 pedestrian detections, 20 were missed (actual pedestrians not ...
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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 ...