in Combinatorial Enumeration A short course

Notes in Combinatorial Enumeration A short course

Half-Century Journey from Synthetic Organic Chemistry to Mathematical Stereochemistry through Chemoinformatics

My half-century journey started from synthetic organic chemistry. During the first stage of my journey, my interest in stereochemistry was initiated through the investigation on the participation of steric effects in reactive intermediates, cylophanes, strained heterocycles, and organic compounds for photography. In chemoinformatics as the next stage of the journey, I proposed the concept of im...

Type-Itemized Enumeration of RS-Stereoisomers of Octahedral Complexes

Stereoisograms of octahedral complexes are classified into five types (type I--typeV) under the action of the corresponding RS-stereoisomeric group. Their enumeration is accomplished in a type-itemized fashion, where Fujita's proligand method developed originally for combinatorial enumeration under point groups (S. Fujita, Theor. Chem. Acc., 113, 73--79 (2005)) is extended to meet the requireme...

Generating the Nine-Point Graphs

A program has been written which recently generated all the (unlabelled) nine-point graphs. Written in MACRO-10 assembly language and run on a 165K PDP10, it generates the complete set of 274,668 graphs in less than six hours. The algorithm on which this program is based is discussed with an emphasis on coding of graphs and various programming techniques designed to save space and time during e...

Systems of Functional Equations and Infinite Dimensional Gaussian Limiting Distributions in Combinatorial Enumeration

In this paper systems of functional equations in infinitely many variables arising in combinatorial enumeration problems are studied. We prove sufficient conditions under which the combinatorial random variables encoded in the generating functions of the system tend to an infinite dimensional Gaussian limiting distribution.