Marked Poset Calculator

Explanation

This webpage is a companion to the paper "Measures on partial orders." It can perform two operations on posets.

The first operation takes a marked poset (P,x) and computes the values of the weak measures λ_p,q and τ on it. It writes down the linear form L(P,x) that expresses the class of (P,x) in terms of the e and j_p,q basis, and also the linear form ell(P,x) one obtains by converting the j's to the variables a, b, p, q, s, t, x, y, z as used in section 5.3 of the paper.

The second operation takes a twice marked poset and computes the polynomial in the a, ..., x variables for its defect. This can be used to obtain the polynomials in Table 3 in section 5.3 of the paper

Input syntax

The poset input is a list of elements, a list of generating inequalities, and—optionally—a list of elements to delete. The app takes the transitive closure first and then passes to the induced order on the undeleted elements.

elements: 1, 2, 3, 4, 5
relations: 1 < 2 < 4, 1 < 3 < 5 < 4
deletions: 5

• elements: is optional, but include it if the poset has isolated elements.
• relations: may use <, <=, >, or >=. Chains such as 1 < 2 < 3 are allowed.
• deletions: is optional and should be followed by a comma-separated list. Those elements are removed after transitive closure, so the calculator uses the induced order on the remaining set.
• Labels should not contain spaces, commas, semicolons, <, >, or #. Text after # is treated as a comment.
• To change the accepted syntax later, edit only the parsePosetText function near the top of the JavaScript section.