Sequences enumerating clutters, antichains, hypertrees, and hyperforests, organized by labeling, spanning, and allowance of singletons. All indices begin at 0. Sequences with ellipses have additional terms in the OEIS. Terms I disagree with are followed by my preferred alternative in square brackets. *** Clutters *** A clutter is a connected antichain of finite nonempty sets (edges). It is spanning if all n vertices are covered by some edge. A clutter with singleton edges allowed is one whose non-singleton edges only are required to form an antichain. Labeled: A305005 (not spanning without singletons): 1, 1, 2, 9, 111, 6829, 7783192, ... A048143 (spanning without singletons): 1, 1[0], 1, 5, 84, 6348, 7743728, ... A304984 (not spanning with singletons): 1, 2, 7, 56, 1533, 210302, 496838435, ... A304985 (spanning with singletons): 1, 1, 4, 40, 1344, 203136, 495598592, ... Unlabeled: A304981 (not spanning without singletons): 1, 1, 2, 5, 19, 176, 16118, 489996568 A261006 (spanning without singletons): 1, 1[0], 1, 3, 14, 157, 15942, 489980450 A304982 (not spanning with singletons): 1, 2, 5, 19, 137 A304983 (spanning with singletons): 1, 1, 3, 14, 118 *** Antichains *** An antichain is a finite set of finite nonempty sets (edges), none of which is a subset of any other. It is spanning if all n vertices are covered by some edge. An antichain with singleton edges allowed is one whose non-singleton edges only are required to form an antichain. Labeled: A006126 (not spanning without singletons): 1, 1, 2, 9, 114, 6894, 7785062, ... A305001 (spanning without singletons): 1, 0, 1, 5, 87, 6398, 7745253, ... A305000 (not spanning with singletons): 1, 2, 8, 72, 1824 A304999 (spanning with singletons): 1, 1, 5, 53, 1577 Unlabeled: A261005 (not spanning without singletons): 1, 1, 2, 5, 20, 180, 16143, 489996795 A304998 (spanning without singletons): 1, 0, 1, 3, 15, 160, 15963, 489980652 A304996 (not spanning with singletons): 1, 2, 6, 24, 166 A304997 (spanning with singletons): 1, 1, 4, 18, 142 *** Hypertrees *** A hypertree is a connected antichain of finite nonempty sets (branches) with no cycles, or equivalently, whose clutter density is -1. It is spanning if all n vertices are covered by some branch. A hypertree with singleton branches allowed is one whose non-singleton branches only are required to form an antichain. Labeled: A305004 (not spanning without singletons): 1, 1, 2, 8, 52, 507, 6844, 118582, ... A030019 (spanning without singletons): 1, 1[0], 1, 4, 29, 311, 4447, 79745, ... A304968 (not spanning with singletons): 1, 2, 7, 48, 621, 12638, 351987, ... A134958 (spanning with singletons): 1, 2[1], 4, 32, 464, 9952, 284608, ... Unlabeled: A304970 (not spanning without singletons): 1, 1, 2, 4, 8, 17, 39, 98 A035053 (spanning without singletons): 1, 1[0], 1, 2, 4, 9, 22, 59, ... A304386 (not spanning with singletons): 1, 2, 5, 15, 50, 200, 907 A134959 (spanning with singletons): 1, 1, 3, 10, 35, 150, 707 *** Hyperforests *** A hyperforest is an antichain of finite nonempty sets (branches) whose connected components are hypertrees. It is spanning if all n vertices are covered by some branch. A hyperforest with singleton branches allowed is one whose non-singleton branches only are required to form an antichain. Labeled: A134954 (not spanning without singletons): 1, 1, 2, 8, 55, 562, 7739, 134808, ... A304911 (spanning without singletons): 1, 0, 1, 4, 32, 351, 5057, 90756, ... A134956 (not spanning with singletons): 1, 2, 8, 64, 880, 17984, 495296, ... A304919 (spanning with singletons): 1, 1, 5, 45, 665, 14153, 399421, ... Unlabeled: A134955 (not spanning without singletons): 1, 1, 2, 4, 9, 20, 50, 128, 351, ... A144959 (spanning without singletons): 1, 0, 1, 2, 5, 11, 30, 78, 223, ... A134957 (not spanning with singletons): 1, 2, 6, 20, 75, 310, 1422 A304977 (spanning with singletons): 1, 1, 4, 14, 55, 235, 1112