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It has been applied to enumeration problems in physics, chemistry, and mathematics.
The answer to many different kinds of enumeration problems can be expressed in terms of binomial coefficients.
Enumeration problems associated with NP-complete problems are NP-hard [24].
To study in depth enumeration problems the class #P was introduced [25].
We illustrate some applications of this method to combinatorial object enumeration problems and bijective combinatorics and discuss an open problem regarding languages having a rational generating function.
For solving vertex and facet enumeration problems we use a Python package pycddlib [ 44], a wrapper of the cddlib (version 094g) that implements the double description method [ 40].
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Similarly, the iterative SAT scheme of Algorithm 1 (see Section 3.1.3) can be adapted to solve credulous reasoning by adding the atom to be queried positively instead of negatively in line 3. Regarding the enumeration problem, Algorithm 2 enumerates all preferred extensions using iterative SAT.
Also, we consider the enumeration problem in which we enumerate all strings corresponding to an input tree and links.
We develop an efficient algorithm for this enumeration problem by extending existing algorithms [13, 14] for enumerating tree-like chemical structures (i.e., chemical structures without cycles).
First, we review some mathematical definitions and give a formal definition of the enumeration problem for chemical structures with monocyclic graph structures.
In this paper, we present a first analytical study of the enumeration problem of perfect matchings on scale-free networks, which are ubiquitous in real-life systems.
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