例句與造句

1. This condition is necessary since every step in a maximal chain is a covering relation, which should change the rank by 1.
2. Richard P . Stanley defines a graded poset of length " n " as one in which all maximal chains have length " n ".
3. This special case of Zorn's lemma is then used to prove the Hausdorff maximality principle, that every poset has a maximal chain, which is easily seen to be equivalent to Zorn's Lemma.
4. Another equivalent characterization of finite join-distributive lattices is that they are graded ( any two maximal chains have the same length ), and the length of a maximal chain equals the number of meet-irreducible elements of the lattice.
5. Another equivalent characterization of finite join-distributive lattices is that they are graded ( any two maximal chains have the same length ), and the length of a maximal chain equals the number of meet-irreducible elements of the lattice.
6. It's difficult to find maximal chain in a sentence. 用maximal chain造句挺難的
7. If " P " also has a greatest element ?( so that it is a bounded poset ), then the previous condition can be simplified to the requirement that all maximal chains in " P " have the same ( finite ) length.
8. A "'branch "'of a tree is a maximal chain in the tree ( that is, any two elements of the branch are comparable, and any element of the tree " not " in the branch is incomparable with at least one element of the branch ).
9. To prove the existence of a partition into a small number of antichains for an arbitrary finite partially ordered set, consider for every element " x " the chains that have " x " as their largest element, and let " N " ( " x " ) denote the size of the largest of these " x "-maximal chains.
10. This definition is given in a context where interest is mostly in finite posets, and although the book subsequently often drops the part " of length " n " ", it does not seem appropriate to use this as definition of " graded " for general posets, because ( 1 ) it says nothing about posets whose maximal chains are infinite, in particular ( 2 ) it excludes important posets like Young's lattice.