star product

The star product of two graded posets (P,P) and (Q,Q), where P has a unique maximal elementMathworldPlanetmath 1^ and Q has a unique minimal element 0^, is the poset P*Q on the set (P1^)(Q0^). We define the partial orderMathworldPlanetmath P*Q by xy if and only if:

  1. 1.

    {x,y}P, and xPy;

  2. 2.

    {x,y}Q, and xQy; or

  3. 3.

    xP and yQ.

In other words, we pluck out the top of P and the bottom of Q, and require that everything in P be smaller than everything in Q. For example, suppose P=Q=B2.


Then P*Q is the poset with the Hasse diagramMathworldPlanetmath below.


The star product of Eulerian posets is Eulerian.


  • 1 Stanley, R., Flag f-vectors and the cd-index, Math. Z. 216 (1994), 483-499.
Title star product
Canonical name StarProduct
Date of creation 2013-03-22 14:09:17
Last modified on 2013-03-22 14:09:17
Owner mps (409)
Last modified by mps (409)
Numerical id 4
Author mps (409)
Entry type Definition
Classification msc 05E99
Classification msc 06A11
Related topic Poset
Related topic GradedPoset