# Tagged Questions

313 views

### Longest of random worm-like paths in $\mathbb{Z}^2$

Imagine at each lattice point of $\mathbb{Z}^2$ within $[1,3n]^2$, with coordinates $\equiv 2 \mod 3$, we place, with equal probability, one of these six patterns:       The result ...
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### Calculate the discrete set of points B which are in the convex hull of the set of points A

This problem is likely best described with the following picture: Given the discrete set of points $A$ (shown in blue), I wish to calculate the discrete set of points that are contained within the ...
254 views

### Hidden points in polygons

Let $h(n)$ be the largest number of mutually invisible points that can be located in a polygon $P$ of $n$ vertices. Two points $x$ and $y$ are mutually invisible if the segment $xy$ contains a point ...
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### Best upper bound on rate for q-ary codes

Among the many upper bounds for families of codes in $\mathbb F _2 ^n$, the best known bound is the one by McEliece, Rodemich, Rumsey and Welch which states that the rate $R(\delta)$ corresponding to ...
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### Optimal Gear Trains

Suppose you need to slow down a turning motor so that a gear turns at an angular velocity $\frac{a}{b}$ of that of the motor shaft, where $a$ and $b$ are natural numbers. For example, this set of ...
491 views

### Minimal blocking objects with shadows like a cube

This is a more geometric version of the previous question, "Lattice-cube minimal blocking sets". I will first specialize to $\mathbb{R}^3$, $d=3$. View an $n \times n \times n$ cube $C_3(n)$ as ...
Let $C_d(n)$ be the lattice cube consisting of the $n^d$ points with each of its $d$ coorindates in $\lbrace 1,2,\ldots,n \rbrace$. Define a blocking set for a lattice cube to be a set of points in ...
Hello, What is a fast way to test whether a partial function can be extended to a chirotope of rank 3 ? That is: I have a domain $E = \{1,...,n\}$ and a partial function $f: E^3 \to \{-1, 0, 1\}$ ...