Now that I am convinced that my post is not a 'homework' type, I am preparing an answer that will take some information from references found. But, my question is, as it is relevant to my answer, is it allowable (or pretentious) to include a link to one of my own published papers?
I don't see anything wrong with it. I would encourage you to make it clear on the post if you have written (or have other connections, i.e. personal, financial or otherwise, with) any of the resources you reference, but I would definitely encourage you to include any and all references you feel are relevant to the post.
That said, you should avoid self-promotion, and if it comes across as that then the community is likely to downvote you, as Manishearth points out.
The community tends to vote down overt self-promotion and flag it as spam. Post good, relevant answers, and if some (but not all) happen to be about your product or website, that’s okay. However, you must [explicitly] disclose your affiliation in your answers. [E.g. it is not enough that your name is mentioned in the link.]
As long as your post doesn't look like one big advertisement or pitch for your work, and you disclose your affiliation, it's OK :)