In How Many Ways Can You Reassemble Several Russian Dolls?

TL;DR

This paper explores the combinatorial problem of reassembling multiple identical Russian dolls, emphasizing the development of algorithms and meta-algorithms for enumerating complex combinatorial arrangements.

Contribution

It introduces new algorithmic approaches and meta-algorithms for counting arrangements of identical objects, inspired by classical combinatorial problems.

Findings

Developed algorithms for counting reassembly arrangements

Extended combinatorial enumeration techniques to complex objects

Proposed meta-algorithm frameworks for combinatorial problems

Abstract

When my brilliant student Thotsaporn "Aek" Thanatipanonda asked me about how many ways can one cover n identical twins, it rang a Bell back to 1981 (see the article). As usual, the method of teaching the computer how to do its own combinatorics, and to use "analysis" (that is really part of discrete math) to enumerate challenging combinatorial objects is even more interesting than the theorems and even the algorithm. Of course, formulas are dead, long live algorithms! But even algorithms are dead, long live meta-algorithms!!