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#!/usr/bin/env perl

...
for my $gene (sort keys %matrix) {
    printf $format, $gene, map { $_ || 0 } @{$matrix{$gene}}{@files};
}

      pm_1079097_File1 pm_1079097_File2 pm_1079097_File3
Gene1                1                0                0
...
Gene4                0                1                1
Gene5                0                0                1
Gene6                0                0                0

$ cat pm_1079097_List
Gene1
...
Gene4
Gene5
Gene6

$ cat pm_1079097_File1
Gene1
Gene2
Gene3

$ cat pm_1079097_File2
Gene2
Gene3
Gene4

$ cat pm_1079097_File3
Gene3
Gene4
Gene5