As title says, what is a deal with omitted results ? Are they equal to supplemental results, and do they have a chance for some SERP's positions ?
Google search uses two types of automatic filters (i.e. omitted results) [reference]. The first is the "Duplicate Snippet Filter", which is often also the Supplemental Index; and the second is the "Duplicate Director Filter", when there are multiple results from the same website (but not Supplemental). Results that are in the "Supplemental Index" will be listed as such, and are generally less likely to appear in search results, unless the query is particulary strange. Best way to get out of the supplemental index is to make sure all the page have a unique meta description tag (aka the "snippet"). Cryo.
I f I have unerstood good, you basically said that omitted are not supplemental, but those filtered as duplicate on one site. In that case, those results should have a chance to rank, am I right ?