All Questions
37
questions with no upvoted or accepted answers
15
votes
0
answers
272
views
Recovering a binary function on a lattice by studying its sum along closed paths
I have a binary function $f:\mathbb N^2\rightarrow\{0,1\}$. While I do not known $f$ explicitly, I have a "device" located at the origin $(1,1)$ which can do the following:
Given an even ...
- 4,333
5
votes
0
answers
45
views
Number of lines of $3$ points in an arrangement of points and lines
It is well known that a finite set of $n$ points cannot form more than
$$\bigg\lfloor \frac{n(n-3)}{6} \bigg\rfloor+1 $$
lines that include $3$ points. Would this result still hold if we assume that ...
user920720
4
votes
0
answers
159
views
Finding simple algorithm to combine students into different groups
I'd like to find an algorithm as simple as possible to solve the problem below.
The same seven students will each day be divided and meet into two groups, one with four students and one with three. ...
- 41
4
votes
0
answers
310
views
Find the number of simple labeled graphs which have no isolated vertices
Find the number of simple labeled graphs on n vertices which have no isolated vertices? Compute the result for n=13
Total number of simple labeled graphs = $2^{n \choose 2}$.
How to remove vertices ...
- 860
4
votes
0
answers
95
views
partitions of finite set in same-size parts having at most one element in common
Given $g \ge 2$, $k \ge 1$ and a population of $p = kg$ workers, I'm trying to figure out the longest series of work shifts such that:
during each shift, all workers work in $k$ teams of g people;
...
- 257
3
votes
0
answers
947
views
Determining Canonical Coin Systems of Five Coins
I need to check whether a given coin system of five coins, $\$ = <1,c_2,c_3,c_4,c_5>$, is canonical, that is, a system in which the greedy algorithm provides the way to make change using the ...
2
votes
0
answers
73
views
Bin packing : item to be packed in a certain bin depend on previously packed items to that bin.
I am working on an engineering problem. I need to implement an algorithm that looks like a certain variant of bin packing. Specifically, in this variant of the bin packing, the size of a certain item ...
- 131
2
votes
0
answers
88
views
Finding all possible valid values of a set based on a list of rules.
I'm working on a programming project and I stumbled into a bit of a problem. I think it's not an impossible problem, but I'm guessing it would involve some math. It would be amazing if anyone can ...
- 121
2
votes
0
answers
56
views
Unique number of combinations after $z$ steps of merging items by specific rules
I encountered an issue where I am trying to estimate the number of unique combinations:
There exists $N$ distinct molecules (or, for example, balls), where each molecule is labelled with some ...
- 21
2
votes
0
answers
50
views
Enumerating separating subcollections of a set
Let $S$ be a (finite) set, and let $C \subseteq 2^S$ be a collection of subsets of $S$. We say that a subcollection $C' \subseteq C$ is separating if for any two elements of $S$ there exists a subset ...
- 11.2k
2
votes
0
answers
70
views
Searching vertices with minimal “variance”
Suppose $\Gamma(V, E)$ is a strongly connected oriented graph and $|V| = n$. Let’s define distance from vertex $v_1$ to vertex $v_2$ as the minimal possible length $d(v_1, v_2)$ of an oriented path ...
- 15.7k
2
votes
0
answers
49
views
Dissecting a hypercube into specific hypercubes
The problem
We define "$m$-cube" as an $m$-dimensional hypercube. ($m=2$ is square, $m=3$ is cube, ...)
$(\mathbf Q):$ Given a container $m$-cube of integer side length $a$, and $n$ many $m$-cubes ...
- 12.5k
2
votes
0
answers
70
views
How many Tromino tilings are there?
Given a $2^k \times 2^k$ grid with $k \geq 1$, it's well known that it's possible to cover the grid minus one (arbitrary) point with $L$-trominoes. The gist of the proof involves considering the four $...
- 12.8k
2
votes
0
answers
702
views
Anti-prime sequence
I have permutation from $x$ to $y$.
And how to make sequence which $d$ summed numbers from this sequence ISN'T a prime number.
if we have sequence $x_1,x_2,x_3,x_4,x_5 \dots y$ than $d$ means :
$x_1+...
- 2,312
1
vote
0
answers
205
views
Find the number of compatibility relations of [n] containing k maximal irredundant set C n,k
Let [n] denote the set of n elements {1, 2, ... , n}. A relation on the set [n] is a subset of the Cartesian product [n] × [n]. Equivalence relations are relations that satisfy self-reflexivity, ...
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