All Questions
40
questions
0
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0
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33
views
Counting matrix paths for (n,m>2) matrices
Given a $n\times m$ matrix with $k$ elements inside it, I need to calculate the number of arrangements of those $k$ elements that form at least 1 path from the top to bottom matrix row composed of the ...
- 111
0
votes
0
answers
82
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The n-th number open problems
Some open problems in mathematics boil down to the question of defining the $n$-th term of a certain sequence for a specific $n$. For instance, the value of the $5$-th diagonal Ramsey number and the $...
- 1,773
1
vote
1
answer
82
views
Percolative process distribution not equivalent to coupon collector problem distribution
I have a process where; given a $n\times 1$ matrix initially empty, an element is inserted in it at a random position, with the possibility of repeating the insertion at a filled cell. Then, after a ...
- 111
0
votes
0
answers
75
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Applications, Generalisations and developments of Green-Tao Theorem after 2018
The well-known Green-Tao Theorem is definitely one of the most striking results among different area of Mathematics such as: Number Theory, Combinatorics, Graph Theory, Ergodic Theory,... etc.
https://...
- 2,498
4
votes
0
answers
108
views
How many connected nonisomorphic graphs of N vertices given certain edge constraints?
Background:
I’m helping a colleague with a theoretical problem in ecology, and I haven’t quite the background to solve this myself. However, I can state the problem clearly, I think:
Problem statement:...
- 341
0
votes
0
answers
74
views
Möbius function for graphs??
I'm reading this post and I'm getting a little confused. I am trying to find a useful notion of the Mobius function for directed graphs and have had little success in my search. I don't know much ...
- 157
0
votes
0
answers
21
views
Finding distinct value that makes up the Integer partition under multiple constraints.
I'm working on a problem that want me to solve for solutions given four equations that is equal to an integer,
For instance, consider the variables $a_1,a_2,\dots,a_m\in \mathbb{Z}_{\geq 0}$ $a_n\neq ...
- 1,071
3
votes
1
answer
75
views
If $1 \leq x_i \leq n$ and $k < n $ what is the value of $\sum_{x_1,x_2,\cdots, x_k \; | \; \sum^k_{i = 1} x_i = n} \sum_{i < j} x_i x_j $
Given positive integers $n$ and $k$ such that $1<k<n$, let $S(n,k)$ be the set of postiive integer $k$-tuples $(x_1,\dots,x_k)$ for which $\displaystyle\sum^k_{i = 1} x_i = n$. For example, $S(5,...
- 131
7
votes
1
answer
189
views
Count pairwise coprime triples such that the maximum number of the triple is not greater than N
Problem Statement:
Given N you are to count the number of pairwise coprime triples which satisfy $1≤a,b,c≤N$.
Example:
For example N=3,
valid triples are (1,1,1),(1,1,2),(1,2,1),(2,1,1),(1,1,3),(1,3,1)...
user1068604
1
vote
1
answer
60
views
Strange limiting value for longest path problem
While I was trying to solve this longest path problem for a directed cyclic graph I posted days ago Longest chain of n-digit square numbers where last digit equals first digit of next, I thought about ...
- 843
4
votes
1
answer
113
views
Freeing banks from debts- a nice combinatorial problem
There are $N$ banks with each having some some (possibly negative) integral balance with them. We say, a bank is in debt if its balance is less than rupee $0$. In each step, a bank may
borrow $1$ ...
- 9,534
1
vote
0
answers
55
views
Recasting Algorithmic Information In Terms of Finite Directed _Cyclic_ Graphs?
Any bit-string {0,1}* can be produced by a finite directed cyclic graph, the nodes of which are n-input NOR functions, with at least two arcs directed away from the graph without a terminal connection ...
- 241
4
votes
1
answer
301
views
Is this a known result on graph products?
Consider two undirected graphs $G=(V,E)$ and $H=(I,F)$.
Denote by $\mathcal N_G(v)$ (resp., $\mathcal N_{H}(i)$) the first neighborhood of a node $v\in V$ (resp., $i\in I$), including $v$ (resp., $i$)....
- 434
1
vote
1
answer
101
views
The number of points in diameters defined by a subdivided hexagon
Just as in the image, imagine that we have $n$ nested hexagons which have subdivided sides just as in the image i.e. the first inner hexagon has no subdivisions, it is just a regular hexagon, the ...
user830143
1
vote
0
answers
33
views
Different slopes defined by nesting $m$ polygons
I know that the vertices of a regular $n$-gon determines the total of $n$ different slopes. We nest the total of $m \in \mathbb{N}$ polygons by drawing a $(1/2)n$-gon inscribed inside the original ...
user830143