We show that Ding's partial order on maximal rook placements on any Ferrers board has a symmetric chain decomposition and is EL-shellable. As a consequence the partial order is Peck, and we show that it has Mobius function values of 1; 0 or +1.

Let G be a simple graph on n vertices. An r-matching in G is a set of r independent edges. The number of r-matchings in G will be denoted by p(G,r). We set p(G,0)=1 and define the matching polynomial of G by μ(G,x):= ∑bn/2c r=0 (−1)·p(G,r)·x and the signless matching polynomial of G by μ(G,x):= ∑bn/2c r=0 p(G,r)·x. It is classical that the matching polynomials of a graph G determine the matchin...

Using bijections between pattern-avoiding permutations and certain full rook placements on Ferrers boards, we give short proofs of two enumerative results. The first is a simplified enumeration of the 3124, 1234avoiding permutations, obtained recently by Callan via a complicated decomposition. The second is a streamlined bijection between 1342-avoiding permutations and permutations which can be...

The rook (Corvus frugilegus L.) is one of the greatest corvine birds dependent on open agricultural land. With the onset of spring, hundreds of thousands of rooks flocks which wintered in Slovakia, this area leaves and returns to its breeding grounds in north-eastern Europe. Wintering populations will be replaced by our rooks, in Slovakia nesting, which wintered in France and Spain. Nesting pop...