Speaker
Luka Podrug
Description
Fibonacci numbers are one of the most famous and investigated sequences. They can be found almost everywhere. For example, the number of ways to tile a $1\times n$ rectangular strip using squares and dominoes is counted by Fibonacci numbers, as is the number of subsets of the set $\left\lbrace 1,2,\dots,n\right\rbrace$ without consecutive elements. Here we consider $2\times n$ hexagonal strips and count the number of ways to divide such strips into a given number of parts. We prove that such divisions are enumerated by the odd-indexed Fibonacci numbers. In this talk, we present three different proofs of this result.
