sigma]] [intersection] ([empty set], S}) the corresponding maximal chain
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
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
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
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.