The “pancake problem” is a well-known open combinatorial problem that recently has been shown to have applications to parallel processing. Given a stack of n pancakes in arbitrary order, all of different sizes, the goal is to sort them into the size-ordered configuration having the largest pancake on the bottom and the smallest on top. The allowed sorting operation is a “spatula flip”, in which...

Unusually long bonds or short intermolecular contacts occur in the title compounds reminiscent of pancake bonding. Pancake bonding interactions seem analogous to π-stacking interactions, but they display much shorter contact distances than normally seen in van der Waals (vdW) dimers. The interpretation of these SN and SeN containing structures has been an outstanding challenge for some time. Th...

π-stacking in dimers of phenalenyl represents the prototypical pancake bonding between radicals. This type of π-stacking aggregate is a key structural motif in conducting organic and multifunctional materials. It is driven by the bonding combination of the singly occupied molecular orbitals (SOMOs) of the monomers resulting in π-stacking contacts that are significantly shorter than the sum of t...

Low dilation embeddings are used to compare similarities between star and pancake networks. The pancake network of dimension n, Pn, has n! nodes, one for each permutation, and an undirected edge between permutations (nodes) when some prefix reversal transforms one permutation into the other. The star network of dimension n, Sn, has n! nodes, one for each permutation, and an undirected edge betw...

In this paper a parallel algorithm for Lagrange interpolation is applied on a n-pancake graph. The npancake graph is a Cayley graph with N=n! vertices and with attractive properties regarding degree, diameter, symmetry, embeddings and self similarity. Using these properties the algorithm carries the calculation in O(N) steps of communication and arithmetic operations instead of O(N) steps for a...

Recently, research on parallel processing systems is very active, and many complex topologies have been proposed. A burnt pancake graph is one such topology. In this paper, we prove that a faulty burnt pancake graph with degree n has a fault-free Hamiltonian cycle if the number of faulty elements is no more than n − 2, and it has a fault-free Hamiltonian path between any pair of non-faulty node...

We prove that a stack of pancakes can be rearranged in all possible ways by a greedy process: Flip the maximum number of topmost pancakes that gives a new stack. We also show that the previous Gray code for rearranging pancakes (S. Zaks, A New Algorithm for Generation of Permutations BIT 24 (1984), 196-204) is a greedy process: Flip the minimum number of topmost pancakes that gives a new stack.