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1.
Application of graph-theoretic methods to new perimeter polynomials for connected clusters on a lattice yields extra data on the total number of clusters and for the coefficients in the series expansion for the mean size of clusters at low densities. The lattices studied are the square, the square with next nearest neighbors, the triangular, and the simple cubic. 相似文献
2.
P. -M. Binder 《Journal of statistical physics》1992,67(3-4):827-832
Average first-passage times for a single-variable stochastic model with a critical fixed point at the origin are computed by exact enumeration. The numerical measurements show excellent agreement with analytical results. The scaling function approaches the predicted asymptotic dependence. 相似文献
3.
Let G=(V,E) be a (directed) graph with vertex set V and edge (arc) set E. Given a set P of source-sink pairs of vertices of G, an important problem that arises in the computation of network reliability is the enumeration of minimal subsets of edges (arcs) that connect/disconnect all/at least one of the given source-sink pairs of P. For undirected graphs, we show that the enumeration problems for conjunctions of paths and disjunctions of cuts can be solved in incremental polynomial time. Furthermore, under the assumption that P consists of all pairs within a given vertex set, we also give incremental polynomial time algorithm for enumerating all minimal path disjunctions and cut conjunctions. For directed graphs, the enumeration problem for cut disjunction is known to be NP-complete. We extend this result to path conjunctions and path disjunctions, leaving open the complexity of the enumeration of cut conjunctions. Finally, we give a polynomial delay algorithm for enumerating all minimal sets of arcs connecting two given nodes s1 and s2 to, respectively, a given vertex t1, and each vertex of a given subset of vertices T2. 相似文献
4.
Damien P. Foster Carlo Vanderzande Julia Yeomans 《Journal of statistical physics》1992,69(3-4):857-868
We study the zero-temperature behavior of several simple models for randomly self-interacting polymers in one and 1+1 dimensions. Results are based on exact enumeration and closed-form expressions. 相似文献
5.
Several sophisticated methods to solution of symmetry specified enumeration problems are available in the modern literature.
In this paper we propose a simple technique that allows one to manually compute the exact numbers of fixed-symmetry derivatives
for a given structure either with inclusion or ignoring the substitution patterns. The basic idea of the method suggested
consists in the derivation of Pólya-like cycle indices for the automorphism groups of specially constructed orbit partition
graphs; the expansion of these indices and subsequent simple calculations result in the desired numbers of substituted derivatives
with achiral substituents. Limitations of the new technique (and a method suggested earlier) depend on the relevance of the
orbit partitions for particular subgroups of the point symmetry group. For illustration purposes, the results obtained for
the prismane (D
3h
) and adamantane (T
d
) structures are discussed. In the former case the numbers of substituted derivatives can be found for all subgroups of the
D
3h
group, whereas in the latter case these numbers can be determined for eight out of eleven subgroups of the T
d
point symmetry group.
This work is based on the text of the lecture presented by the authors at the 5th All-Russia Conference on Molecular Modeling
(Moscow, April 2007). The paper deals with the methodology and detailed treatment of applied aspects related to solution of
enumeration problems for substituted derivatives with prescribed symmetry groups. Unlike the known methods of symmetry specified
enumeration, the technique suggested is simple enough and may be regarded as generalization of the Pólya methodology, which
is widely used by chemists.
Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 227–245, February, 2008. 相似文献
6.
Multiple zigzag chains of length n and width m constitute an important class of regular graphene flakes of rectangular shape. The physical and chemical properties of these basic pericondensed benzenoids can be related to their various topological invariants, conveniently encoded as the coefficients of a combinatorial polynomial, usually referred to as the ZZ polynomial of multiple zigzag chains . The current study reports a novel method for determination of these ZZ polynomials based on a hypothesized extension to John–Sachs theorem, used previously to enumerate Kekulé structures of various benzenoid hydrocarbons. We show that the ZZ polynomial of the multiple zigzag chain can be conveniently expressed as a determinant of a Toeplitz (or almost Toeplitz) matrix of size consisting of simple hypergeometric polynomials. The presented analysis can be extended to generalized multiple zigzag chains , i.e., derivatives of with a single attached polyacene chain of length k. All presented formulas are accompanied by formal proofs. The developed theoretical machinery is applied for predicting aromaticity distribution patterns in large and infinite multiple zigzag chains and for computing the distribution of spin densities in biradical states of finite multiple zigzag chains . 相似文献
7.
Summary The [h]phenylene C6h
H2h+4 isomers are enumerated up toh=12. The numbers are compared with old and new data for C
n
H5 isomers of benzenoids, fluoranthenoids and biphenylenoids.
Anzahl möglicher Isomerer von Phenylenen
Zusammenfassung Die Anzahl der [h]Phenylen-Isomeren C6h H2h+4 wurde bish=12 ausgewertet. Die Zahlen wurden mit alten und neuen Daten für C n H s -Isomere von Benzenoiden, Fluoranthenoiden und Biphenyloiden verglichen.相似文献
8.
9.
A priority queue transforms an input permutation of some set of sizen into an output permutation. It is shown that the number of such pairs (, ) is (n + 1)
n–1. Some related enumerative and algorithmic questions are also considered.Supported by the National Science and Engineering Research Council of Canada under Grant A4219. 相似文献
10.
Shinsaku Fujita 《Theoretical chemistry accounts》2007,117(3):353-370
Planted three-dimensional (3D) trees, which are defined as a 3D version of planted trees, are enumerated by means of Fujita’s
proligand method formulated in Parts 1–3 of this series [Fujita in Theor Chem Acc 113:73–79, 80–86, 2005; Fujita in Theor
Chem Acc 115:37–53, 2006]. By starting from the concepts of proligand and promolecule introduced previously [Fujita in Tetrahedron
47:31–46, 1991], a planted promolecule is defined as a 3D object in which the substitution positions of a given 3D skeleton are occupied by a root and proligands.
Then, such planted promolecules are introduced as models of planted 3D-trees. Because each of the proligands in a given planted
promolecule is regarded as another intermediate planted promolecule in a nested fashion, the given planted promolecule is
recursively constructed by a set of such intermediates planted promolecules. The recursive nature of such intermediate planted
promolecules is used to derive generating functions for enumerating planted promolecules or planted 3D-trees. The generating
functions are based on cycle indices with chirality fittingness (CI-CFs), which are composed of three kinds of sphericity
indices (SIs), i.e., a
d
for homospheric cycles, c
d
for enantiospheric cycles, and b
d
for hemispheric cycles. For the purpose of evaluating c
d
recursively, the concept of diploid is proposed, where the nested nature of c
d
is demonstrated clearly. The SIs are applied to derive functional equations for recursive calculations, i.e., a(x), c(x
2), and b(x). Thereby, planted 3D-trees or equivalently monosubstituted alkanes as stereoisomers are enumerated recursively by counting
planted promolecules. The resulting values are collected up to 20 carbon content in a tabular form. Now, the enumeration problem
initiated by mathematician Cayley [Philos Mag 47(4):444–446, 1874] has been solved in such a systematic and integrated manner
as satisfying both mathematical and chemical requirements. 相似文献