> The definition of grading is that all maximal chains of every interval > have the same length. This is given in the above poset, but sage says > it is not graded.
The problem here is what people consider a "rank function" on a poset. Do we want that all minimal elements have value 0 ? Then your poset is indeed not graded. Or do we only want that some element has value 0 ? Then your poset is graded. But if we take the later, what are then the "levels" of a poset? Are all minimal elements in level 0 (which seems to me like a good choice), or are the levels given by your grading? I think you're right since the existence of a rank function seems to be common sense as the definition (http://en.wikipedia.org/wiki/Graded_poset) (this is equivalent to your definition for locally finite posets). But then, we have to make a choice for the levels of a poset. My 2 cents, Christian -- You received this message because you are subscribed to the Google Groups "sage-combinat-devel" group. To post to this group, send email to sage-combinat-devel@googlegroups.com. To unsubscribe from this group, send email to sage-combinat-devel+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sage-combinat-devel?hl=en.
