This section is from the book "An Illustrated Flora Of The Northern United States, Canada And The British Possessions Vol1", by Nathaniel Lord Britton, Addison Brown. Also available from Amazon: An Illustrated Flora of the Northern United States, Canada and the British Possessions. 3 Volume Set..
Carex polygama Schkuhr, Reidgr. 1: 84. 1801. Not J. F.
Glabrous, culms aphyllopodic, strongly filamentose, stiff, erect, sharp-angled, rough above, 8'-3° tall. Leaves rough, erect, 1"-2" wide, shorter than or exceeding the culm; spikes 2-7, oblong or cylindric, erect, all sessile and close together or the lowest sometimes distant and very short-stalked, 4"-2o" long, about 4" in diameter when mature, the terminal staminate at base or rarely throughout; perigynia elliptic or somewhat obovate, flat, ascending, 1 1/2"-2" long, very light green, granular, faintly nerved, beakless, the apex minutely 2-toothed; scales ovate, awn-tipped, black or dark brown with a green midvein, longer than the perigynia; stigmas 3.
In bogs, Greenland to Alaska, south to Georgia, Kentucky, Missouri, Utah and California. Also in Europe and Asia. May-July.
Carex Shortiana Dewey, Am. Journ. Sci. 30: 60. 1836,
Glabrous, culms rather slender, erect, rough above, l°-3° tall, usually overtopped by the upper leaves. Leaves elongated, roughish, 2"~4' wide; bracts short, narrow, the lowest little sheathing; spikes 3-7, gynae-candrous, linear-cylindric, densely many-flowered, 1/2'-1 1/2 long, 2"-2 1/2" in diameter, erect, the lower stalked, the uppermost staminate below for about one-half its length; perigynia spreading, orbicular or obovate, 1" long, darkened at maturity, compressed, 2-edged, nerveless, slightly wrinkled, ridged at apex, abruptly and minutely beaked, the orifice entire or nearly so; scales ovate or oblong-lanceolate, scarious-margined, acute, acuminate, or obtusish and cuspidate, persistent, shorter or longer than perigynia; stigmas 3.
Glabrous, light green and glaucous, culms stout, phyllopodic, erect, much roughened on the angles above, 1 1/2°-4° tall. Leaves 8-15 to a culm, flat or in drying somewhat involute, rough, 11/2"-3" wide, usually exceeded by the culm, tapering to a very long narrow tip, the basal sheaths not filamentose; lower bracts similar, shorter; staminate spike usually I, long-stalked, the scales short-awned; pistillate spikes 3-5. cylindric, dense, 15-50-flowered, 7"-15" long, 4" thick, little separate, erect, sessile or the lower stalked; perigynia dark brown, slightly glaucous, squarrose, broadly ovoid, 3-angled, 2 long, 1 1/2"-1 3/4" wide, strongly ribbed, abruptly contracted into a sharp beak about one-fourth as long as the body,the orifice entire; scales oblong-ovate, scarious-margjned, abruptly awned, from slightly exceeding to much shorter than perigynia; stigmas 3.
In swamps, Missouri to Florida and Texas. June-Aug.