maximal chain

maximal chain

[¦mak·sə·məl ′chān]
(mathematics)
A sequence of n + 1 subsets of a set of n elements, such that the first member of the sequence is the empty set and each member of the sequence is a proper subset of the next one.
References in periodicals archive ?
sigma]] [intersection] ([empty set], S}) the corresponding maximal chain of [[?
However, 33 of the 49 remaining nodes contain the letter 'i', so the maximal chain can be no longer than 2(49-33) + 1 = 33 by the alternating letter argument.
If there exists a maximal chain consisting of left-modular elements, then P is called left-modular.
The rank rk(x) is the length r of a maximal chain [C.
Moreover, by the standard chain decomposition of network flows of Ford Jr and Fulkerson (2010) (essentially Stanley's transfer map), which expresses g as a sum of positive flows through each maximal chain of P, it is clear that for A an antichain of P, we have that e(P) [greater than or equal to] [[summation].
P]) be a bounded poset and let c : [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] be a maximal chain of P.
It can be shown, however, that any maximal chain c [member of] M([[PI].
In particular, we say that a maximal chain C in SP(u, v) is rising if the path corresponding to C in B(u, v) is rising.
In this situation, we say that C is a maximal chain for e.
Recall that a finite poset is called graded, if all maximal chains are of the same length.
Classically, binomial posets are infinite posets with the property that every two intervals of the same length have the same number of maximal chains.
We say that P is graded if all maximal chains of P have the same length and call this length the rank of P.
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