From between 2006-2012, a series of books was published by a Turkish electrical engineer and hadith scholar called Halis Aydemir.
In them, he asserts that splitting the Quran in various categories always provides a perfectly symmetrical result.
Odd-Odd means Odd number of verses and an odd sequence number, even-even means even number of verses and an even sequence number and so on.
However, the examples presented here don't do justice to everything given by the author in his books. Parts 1-2 can be read here here, part 3 can be read here and part 4 can be read only on author's website here (Turkish).
Are the findings really significant? What would the probability be to find them in a randomly generated set of surah numbers and verse (ayat) numbers?