Arctic Curves Phenomena for Bounded Lecture Hall Tableaux

The Lecture Hall Parallelepiped

The s-lecture hall polytopes Ps are a class of integer polytopes defined by Savage and Schuster which are closely related to the lecture hall partitions of Eriksson and Bousquet-Mélou. We define a half-open parallelopiped Pars associated with Ps and give a simple description of its integer points. We use this description to recover earlier results of Savage et al. on the δ-vector (or h∗-vector)...

Anti-Lecture Hall Compositions

We study the set Ak of integer sequences = ( 1; : : : ; k), de ned by 1 1 2 2 : : : k k 0; and show that the generating function is X 2Ak q j = k Y

Lecture 23 : Resonance Phenomena

Lecture 9 Threshold Phenomena

Though our main technical result concerns random graphs in the G(n,p) model, let us mention other contexts in which threshold phenomena occur. One classical example is Percolation, an area started in physics. A typical question here is this: given a planar grid and 0 < p < 1. Create a graph by keeping each edge of the planar grid with probability p and removing each edge with probability 1-p. T...

Skew Tableaux, Lattice Paths, and Bounded Partitions

We establish a one to one correspondence between a set of certain bounded partitions and a set of two-rowed standard Young tableaux of skew shape. Then we obtain a formula for a number which enumerates these partitions. We give two proofs for this formula, one by applying the above correspondence, the other by using the reflection principle. Finally, we give another expression for this number i...