Just added! Took me awhile to figure that out-I tried to edit the post about 8 times and include the photos! :)

Setaria sp ?

because of the "folded" leaves (cross section shaped like a wide "M"?) I would lean towards Carex, sedge

the flower could be that of a monoecious species, probably female flower.

if you look from the top at a Carex plant, the leaves are typically spread out in three parts with equal distances between them

Some kind of sedge I would guess. Is the stem 3 sided?

You may be more likely to get suggestions if you give us a general location such as nearest large city, though no guarantees.

whenever i see aggressive seed production... i wonder if there is a bird feeder around .... which might narrow it down to bird seed plants ...

ken

Definitely one of the many Carex species. If I saw that in Arkansas, I would suspect C. lupulina. However, there are several that appear similar.

thedecoguy: I actually don't think it's setaria. I googled that and realized we do have that other places in our yard, but this one is different. But thanks for the suggestion, because now I know what those other plants are too.

linaria_gw, NHBabs z4b-5a NH, and jekeesl (south-central Arkansas): Yes! I'm positive it is a sedge. Thank you! I'm leaning toward Carex squarrosa (found this helpful page: http://www.herbarium.lsu.edu/keys/carex/carex.html) but not 100% sure. Knowing it is a sedge is super helpful, though.

ken_adrian: no bird feeder around here, but there has been a bag of birdseed in our garage since we moved in that mice have gotten into. Is sedge a seed that's commonly in birdseed?

Next question: In my vegetable garden, we have had trouble with terrible drainage due to thick, sticky soil. We have slightly raised beds and the dirt in those is improving, but the paths between the beds are constantly muddy. Do you think transplanting sedge into the pathways, and then keeping it mowed low would be a way to let plant roots take up some of that water? Or would the sedge be able to invade my veggie beds and I'd regret introducing it? Thanks!

I would skip the gravel if it were mine and put down a good layer of coarse mulch. I don’t think planting will make it any less wet.