1
$\begingroup$

I am from math.stackexchange, here is my original post.

https://math.stackexchange.com/questions/2354828/anagrams-prime-numbers-and-prime-number-coding

The only comment I received was too technical for me, so I've decided to repost here in hope of a more mathematician friendly answer. Thanks in advance!


A while back I realised that I could find all anagrams in a language by assigning each letter to a prime number (I call this prime coding, though it probably has a proper name) then multiply the letters in a word to create some value. Then words that are anagrams will have the same value.

for example, if we let: $$a=2, \;\; b=3, \;\; c=5, \;\; d=7, \;\; \cdots , \;\; t=71, \;\; \cdots$$ then $cat = 2\times 5 \times 71$ and $tac = 71 \times 2 \times 5$

Due to the fundamental theorem of arithmetic two words will have the same value if and only if they are anagrams.

When I thought about this practically, the numbers started getting pretty big. A 10 letter word is likely to be over 1 trillion. In an attempt to reduce these values I turned to Gaussian Integers. So that I could use smaller numbers as my primes.

  • Are there any more types of prime numbers I could use to further reduce values?

I suspect Quarternions and Octonians(?) and further powers of 2 down that route could potentially reduce the value at a cost of the number of numbers needed. So presumably there would be an optimal pay off here. But I'm more interested in a different approach.

Thank you in advance

$\endgroup$

closed as off-topic by Yuval Filmus, domotorp, Gamow, Emil Jeřábek, Aryeh Feb 26 at 14:52

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "Your question does not appear to be a research-level question in theoretical computer science. For more information about the scope, please see help center. Your question might be suitable for Computer Science which has a broader scope." – Yuval Filmus, domotorp, Gamow, Emil Jeřábek, Aryeh
If this question can be reworded to fit the rules in the help center, please edit the question.

Browse other questions tagged or ask your own question.