proposed

approved

editing

proposed

Ran Pan, <a href="http://www.math.ucsd.edu/~r1panprojectp/problems/p1.html">Problem 1</a>, Project P.

Ran Pan, <a href="http://www.math.ucsd.edu/~r1panprojectp/problems/solutions/OneLevelGridPoset.pdf">Algorithmic Solution to Problem 1 (and linear extensions of general one-level grid-like posets)</a>, Project P.

approved

editing

editing

approved

The definition of a one-level grid poset can be found in the Pan links. The number of linear extensions of one-level grid poset G[(0^n), (0^(n-1)), (0^(n-1))] is given by Catalan number A000108(n), the number of linear extensions of the one-level grid poset G[(1^n), (0^(n-1)), (0^(n-1))] is given by A274644(n) and number of linear extensions of the one-level grid poset G[(2^n), (0^(n-1)), (0^(n-1))] is counted given by A274645(n).

proposed

editing

editing

proposed

The definition of a one-level grid poset can be found in the Pan links. The number of linear extensions of one-level grid poset G[(0^n), (0^(n-1)), (0^(n-1))] is given by Catalan number A000108(n), the number of linear extensions of the one-level grid poset G[(1^n), (0^(n-1)), (0^(n-1))] is given by A274644(n) and number of linear extensions of the one-level grid poset G[(2^n), (0^(n-1)), (0^(n-1))] is counted by A274645(n).

proposed

editing

editing

proposed

The definition of a one-level grid poset can be found in Pan links. The number of linear extensions of one-level grid poset G[(0^n), (0^(n-1)), (0^(n-1))] is given by Catalan number A000108(n), the number of linear extensions of the one-level grid poset G[(1^n), (0^(n-1)), (0^(n-1))] is given by A274644(n) and number of linear extensions of the one-level grid poset G[(2^n), (0^(n-1)), (0^(n-1))] is counted by A274645(n).

Number of linear extensions of the one-level grid poset G[(3^n), (0^(n-1)), (0^(n-1))].

The definition of a one-level grid poset can be found in Pan's link links. Number The number of linear extensions of one-level grid poset G[(0^n), (0^(n-1)), (0^(n-1))] is counted given by Catalan number A000108, (n), the number of linear extensions of the one-level grid poset G[(1^n), (0^(n-1)), (0^(n-1))] is counted given by A274644 (n) and number of linear extensions of one-level grid poset G[(2^n), (0^(n-1)), (0^(n-1))] is counted by A274645(n).

proposed

editing