Trivial Chain

Hey there. I was looking around but could not find it: what is the number of chains in a “degenerate” interval of a poset? Thank you!

Advertisements

3 comments

  1. I assume that by “degenerate” interval you mean the trivial interval, namely [x, x], for $x$ in a poset. In this case, there is only one possible chain contained in [x, x], namely C = {x}.

    • Sorry, I had a few typos in my reply. Below I repeat the second sentence:

      In this case, there is only one possible chain contained in [x, x], namely C = \{x\}.

      (Recall that a chain C is a subset of a poset where any two elements in C are related, or “comparable.”)

  2. sammonkie

    Got you,thank you! 😉

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: