  Sequence organizations are viewed from two points: one is from informational
redundancy or informational correlation (IC) and another is from k-mer
frequency statistics. Two problems are investigated. The first is how the ICs
exceed the fluctuation bound and the order emerges from fluctuation in a genome
when the sequence length attains some critical value. We demonstrated that the
transition from fluctuation to order takes place at about sequence length
200-300 thousands bases for human and E coli genome. It means that the life
emerges from a region between macroscopic and microscopic. The second is about
the statistical law of the k-mer organization in a genome under the
evolutionary pressure and functional selection. We deduced a sum rule Q(k,N) on
the k-mer frequency deviations from the randomness in a N-long sequence of
genome and deduced the relations of Q(k,N) with k and N. We found that Q(k,N)
increases with length N at a constant rate for most genome sequences and
demonstrated that when the functional selection of k-mers is accumulated to
some critical value the ordering takes place. An important finding is the sum
rule correlated with the evolutionary complexity of the genome.
