Build an array of arrays: 
my @segments = map [split //], @genome;

[download]

Now $segments[$i] will be a reference to an array containing the chars of $genome[$i], so you can access individual chars with $segments[$i][$j] (where $i is the segment index and $j is the part number), or the entire array of chars of one segment with @{$segments[$i]}.

For example, this code: 

my @genome = ("abc", "def", "ghijkl");
my @segments = map [split //], @genome;
for my $seg (@segments) {
    print "Segment: @$seg\n";
}

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will output: 
Segment: a b c
Segment: d e f
Segment: g h i j k l

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See perldoc perllol for more details.

•Update: a few corrections and a bit more explanation

In reply to Re: splitting every element of an array by xmath
in thread splitting every element of an array by Anonymous Monk

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