Mathematical Combinatorics Vol 2 2009

This volume contains a colection of articles on smarandache notions in graph theory, combinatorics.

Topics in detail to be covered are: Smarandache multi-spaces with applications to other sciences, such as those of algebraic multi-systems, multi-metric spaces; Smarandache geometries; Differential Geometry; Geometry on manifolds; Topological graphs; Algebraic graphs; Random graphs; Combinatorial maps; Graph and map enumeration; Combinatorial designs; Combinatorial enumeration; Other applications of Smarandache multi-space and combinatorics.

Papers by many authors about the Smarandache Bol Loops, Smarandachely Precontinuous maps and Preopen Sets, Smarandache quasigroups and loops, Smarandache right inverse, Smarandache bijections, Smarandache permutation(symmetric) group[S-permutation group], Smarandache path k-cover, Smarandache space, Smarandache k-tiling, Smarandachely dominating k-set, Smarandache graphoidal tree (k, d)-cover of a graph, Smarandache k-orientation, Smarandache k-tree, Smarandache k-orientation, Smarandache geometries etc.

Papers on Smarandachely Bondage Number of a Graph, Domination Number in 4-Regular Graphs, On Smarandachely Harmonic Graphs, Independent Complementary Distance Pattern Uniform Graphs, Efficient Domination in Bi-Cayley Graphs, and other topics. Contributors: D.D. Somashekara, C.R. Veena, Aysun Aytac, Elgin Kilic, Agboola A.A.A., D Akinola L.S., K. R. Vasuki, G. Sharath, E. Sampathkumar, P. Siva Kota Reddy, M.S. Subramanya, Liangxia Wan, Hongjian Lai, Yanpei Liu, and others

Topics in detail to be covered are: Smarandache multi-spaces with applications to other sciences, such as those of algebraic multi-systems, multi-metric spaces; Smarandache geometries; Differential Geometry; Geometry on manifolds; Combinatorial designs; Combinatorial enumeration; Other applications of Smarandache multi-space and combinatorics.

Richard Stanley's two-volume basic introduction to enumerative combinatorics has become the standard guide to the topic for students and experts alike. This thoroughly revised second edition of volume two covers the composition of generating functions, in particular the exponential formula and the Lagrange inversion formula, labelled and unlabelled trees, algebraic, D-finite, and noncommutative generating functions, and symmetric functions. The chapter on symmetric functions provides the only available treatment of this subject suitable for an introductory graduate course and focusing on combinatorics, especially the Robinson–Schensted–Knuth algorithm. An appendix by Sergey Fomin covers some deeper aspects of symmetric functions, including jeu de taquin and the Littlewood–Richardson rule. The exercises in the book play a vital role in developing the material, and this second edition features over 400 exercises, including 159 new exercises on symmetric functions, all with solutions or references to solutions.

The mathematical combinatorics is a subject that applying combinatorial notion to all mathematics and all sciences for understanding the reality of things in the universe. The International J. Mathematical Combinatorics is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences and published in USA quarterly, which publishes original research papers and survey articles in all aspects of mathematical combinatorics, Smarandache multi-spaces, Smarandache geometries, non-Euclidean geometry, topology and their applications to other sciences.

Papers on Problems of Persons with Disability (PWD) Using FRMs, Topological Multi-groups and Multi-fields, Involute and Evolute Curves of Spacelike Curve with a Spacelike Principal Normal in Minkowski 3-Space, Smarandache Breadth Pseudo Null Curves in Minkowski Space-time, and similar topics. Contributors: W.B. Vasantha Kandasamy, A.Praveen Prakash, K. Thirusangu, Bahaddin Bukcu, Murat Kemal Karacan, Shreedhark, B. Sooryanarayana, and others.