tag:blogger.com,1999:blog-6555947.post3822396270372210766..comments2022-11-14T21:35:50.440-07:00Comments on The Geomblog: Name of a kind of weight function on a lattice ?Suresh Venkatasubramanianhttp://www.blogger.com/profile/15898357513326041822noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-6555947.post-29982571251456452272008-06-05T09:15:00.000-06:002008-06-05T09:15:00.000-06:00I don't know of a name for such a function, but it...I don't know of a name for such a function, but it sounds like it would be easiest to consider as a probability measure on the lattice, considered as a set of subsets of max.<BR/><BR/>Then you can notice that not all lattices will allow you to satisfy a strict inequality x > y implies w(x) > w(y); but you can also classify which lattices force this inequality to be non-strict. Intuitively, I guess it's possible iff the lattice is countable.<BR/><BR/>From this line of thinking, you can also analyze your degrees of freedom in choosing w. For example, you can assign an arbitrary nontrivial weight to an arbitrary non-min/max element to begin with. This is more of a guess, but you might even be able to uniquely classify the weight by assigning arbitrary nontrivial values to a strong antichain with join = max. By "strong antichain" I mean that no pairwise meet is min.Tylerhttps://www.blogger.com/profile/15571626397230878686noreply@blogger.comtag:blogger.com,1999:blog-6555947.post-8265523877558626312008-06-05T01:03:00.000-06:002008-06-05T01:03:00.000-06:00sub-additive (monotone)sub-additive (monotone)Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6555947.post-6419244245007516962008-06-04T21:37:00.000-06:002008-06-04T21:37:00.000-06:00it sounds like a measure function?it sounds like a measure function?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6555947.post-39254657735616874962008-06-04T19:16:00.000-06:002008-06-04T19:16:00.000-06:00subadditive increasing?subadditive increasing?Anonymousnoreply@blogger.com