Can anyone suggest a simple and efficient way (preferably embodied in computer code) to compute the average height function for lozenge tilings of an $a,b,c,a,b,c$ semiregular hexagon? I prefer to ...
Same way as the two dimensional tilings by rhombi come from minimal surfaces in a $D$ dimensional cubical lattice as mentioned in this answer, one can consider higher dimensional zonotopes tiled by ...
Hi all, I am doing a work in collaboration with other mathematicians about phase transition in the Ising model and we need to know if exponential upper bounds exist for the number of lattice animals ...
Consider graph $T$ where nodes correspond to maximal cliques of some graph $G$ and two nodes can be connected if corresponding cliques intersect. Clique tree is an example when $T$ is required to be a ...
Background I study polymer physics and am doing experiments testing the model outlined in this paper. Basically, the polymers fall into an integer number of pits, and we create a partition function ...
Suppose we have an undirected graph with integer valued nodes where $0<|i-j|\le 2$ implies nodes $i$ and $j$ are connected. Let $c_n$ be the number of self-avoiding walks on this graph of length ...
I recently read the following "open problem" titled "Pennies on a carpet" in "An Introduction To Probability and Random Processes" by Baclawski and Rota (page viii of book, page 10 of following ...
In 1986 G.X. Viennot published "Heaps of pieces, I : Basic definitions and combinatorial lemmas" where he developed the theory of heaps of pieces, from the abstract: a geometric interpretation of ...