symmetric chain

symmetric chain

[sə¦me·trik ′chān]
(mathematics)
A sequence of subsets of a set of n elements such that each member of the sequence is a subset of the next one, each member of the sequence has a cardinality one greater than that of the previous member, and the sum of the cardinalities of the first and last members of the sequence equals n.
References in periodicals archive ?
However, O'Hara's construction does not give a symmetric chain decomposition of the poset L(l, m) of partitions which fit the l x m rectangle (in other words, the difference between successive partitions is not always a corner).
5, which might lead to a way of finding a symmetric chain decomposition of the poset L(m, l) mentioned above.
On the other hand, cases l = 3, 4 have been studied in [Lin, W] using an explicit symmetric chain decomposition.
Wen, Computer-generated symmetric chain decompositions for L(4, n) and L(3, n), Adv.
Since any product of chains is a symmetric chain order, [C.