Permutations that can be sorted greedily by one or more stacks having various constraints have been studied a number of authors. A pop-stack is greedy stack must empty all entries whenever popped. in the image operator are said to pop-stacked. Asinowki, Banderier, Billey, Hackl, and Linusson recently investigated these permutations calculated their up length 16. We give polynomial-time algorith...

The class of generalized satisfiability problems, introduced in 1978 by Schaefer, presents a uniform way of studying the complexity of satisfiability problems with special conditions. The complexity of each decision and counting problem in this class depends on the involved logical relations. In 1979, Valiant defined the class *P, the class of functions definable as the number of accepting comp...

I owe this almost atrocious variety to an institution which other republics do not know or which operates in them in an imperfect and secret manner: the lottery. So far, our approach to computing devices was somewhat conservative: we thought of them as executing a deterministic rule. A more liberal and quite realistic approach , which is pursued in this chapter, considers computing devices that...

Counting problems are studied in a variety of areas. For example, enumerative combinatorics, statistics, statistical physics, and artificial intelligence. In this dissertation, we investigate several counting problems, which are subjects of active research. The specific problems considered are: counting independent sets in bipartite graphs (#BIS), computing the partition function of the hard-co...

We analyze the complexity of Node Counting, a graph-traversal method. On many graphs arising in control problems in Artificial Intelligence, Node Counting performs as efficiently as other methods which are known to be of polynomial complexity in the number of states (e.g., Learning Real-Time A* method). We show that complexity of Node Counting on undirected graphs is (n p ), which is not polyno...

We use Wagner's weighted subgraph counting polynomial to prove that the partition function of anti-ferromagnetic Ising model on line graphs is real rooted and roots edge cover have absolute value at most $4$. more generally show a $k$-uniform hypergraph $2^k$, discuss applications this domination polynomials graphs. moreover how our results relate efficient algorithms for approximately computin...

A simple decomposition for graphs yields generating functions for counting graphs by edges and connected components. A change of variables gives a new interpretation to the Tutte polynomial of the complete graph involving inversions of trees. The relation between the Tutte polynomial of the complete graph and the inversion enumerator for trees is generalized to the Tutte polynomial of an arbitr...

We define a trivariate polynomial combining the NL-coflow and NL-flow polynomial, which build dual pair counting acyclic colorings of directed graphs, in more general setting regular oriented matroids.