engleski

Combinatorics of diagonally convex directed polyominoes

A new bijection between diagonally convex directed (ded-) polyominoes and ternary trees makes it possible to enumerate the ded-polyominoes according to several parameters (sources, diagonals, horizontal and vertical edges, target cells). For a part of these results we also give another proof, which is based on Raney's generalized lemma. Thanks to the fact that the diagonals of ded-polyomino can grow at most by one, the problem of $q$-enumeration of this object can be solved by an application of Gessel's $q$-analog of the Lagrange inversion formula.

ded-polyomino; $q$-enumeration; Lagrange inversion formula Gessel's $q$-analog

nije evidentirano