.svg){kind=logo}
GENERALIZED PASCAL’S PYRAMIDS AND COMBINATORIAL INFORMATION RETRIEVAL PROBLEMS
Keywords:
hierarchical structure, partially ordered set, generalized Pascal’s pyramid, generalized Stirling’s numbers, information retrieval problems, relevance indexDOI:
https://doi.org/10.17654/0974165824043Abstract
The work studies combinatorial objects of pyramidal structure. It proposes fundamental relations for generalizations of Pascal’s triangle and pyramid. It considers problems of finding new ways of constructing information relevance indices and offers a way of constructing such an index with the help of Pascal’s generalized pyramids. Using structures of a type of Pascal’s generalized pyramids with weight factors allow construction of an index that reflects a degree of relevance of keywords, as well as makes it possible to allocate subsets of keywords with specific properties.
The offered methods of the combinatorial analysis of hierarchical structures in information retrieval problems can be used in creating and analyzing knowledge databases.
Received: February 3, 2024
Accepted: July 24, 2024
References
M. Mesarovic, D. Mako and Y. Takahara, Theory of Hierarchical Multilevel Systems, Academic Press, New York, 1970, 294 pp.
T. L. Saaty, The Analytic Hierarchy Process: Planning, Priority Setting, Resource Allocation, McGraw-Hill, New York, 1980, 287 pp.
Marvin L. Manheim, Hierarchical Structure: A Model of Design and Planning Processes, MIT Press, Cambridge, 1966, 227 pp.
O. V. Kuzmin and V. I. Martyanov, Combinatorial-logical Methods of Analysis of Hierarchical Structures and Development of Intelligent Decision Support Systems, Irkutsk University Press, Irkutsk, 2022, 199 pp. (in Russian).
R. P. Stanley, Enumerative Combinatorics, Vol. 1, Cambridge University Press, Cambridge, 1997, 335 pp.
G. Gratzer, Lattice Theory: Foundation, Springer, Basel AG, 2011, 644 pp.
George E. Andrews, Christian Krattenthaler and Alan Krinik, eds., Lattice Path Combinatorics and Applications, Springer, 2019, 418 pp.
William T. Trotter, Combinatorics and Partially Ordered Sets: Dimension Theory, Johns Hopkins University Press, London, 1992, 328 pp.
A. A. Balagura and O. V. Kuzmin, Generalized Pascal’s pyramid and partially ordered sets, Surveys on Applied and Industrial Mathematics 14(1) (2007), 88-91 (in Russian).
V. B. Lebedev and E. A. Fedotov, Information system data modeling using the lattice theory methods, University Proceedings, Volga Region, Engineering Sciences, 2015, pp. 104-110 (in Russian).
S. K. Murthy, Automatic construction of decision trees from data: a multidisciplinary survey, Data Min. Knowl. Discov. 2(4) (1998), 345-389.
O. V. Kuzmin, Generalized Pascal Pyramids and their Applications, Nauka Publ., Novosibirsk, 2000, 294 pp. (in Russian).
O. V. Kuzmin, A. A. Balagura, V. V. Kuzmina and I. A. Khudonogov, Partially ordered sets and combinatory objects of the pyramidal structure, Advances and Applications in Discrete Mathematics 20(2) (2019), 229-242.
R. F. Ahlswede and I. Wegener, Search Problems, John Wiley & Sons, New York, 1987, 296 pp.
P. I. Braslavskiy, E. A. Vovk and M. Yu. Maslov, Faceted organization of the internet catalogue and automatic classification of documents by genre: proceedings of international seminar “Dialogue-2002”, Vol. 2, Computer Linguistics and Intellectual Technologies, Nauka Publ., Moscow, 2002, pp. 83-93 (in Russian).
T. J. Theorey and J. P. Fry, Design of Database Structures, Prentice-Hall, Englewood Cliffs, New York, 1982, 492 pp.
A. A. Balagura and O. V. Kuzmin, Generalized Pascal pyramids and their reciprocals, Discrete Math. Appl. 17(6) (2007), 619-628.
B. A. Bondarenko, Generalized Pascal Triangles and Pyramids, their Fractals, Graphs, and Applications, The Fibonacci Association, Santa Clara, 2010, 296 pp.
O. V. Kuzmin and M. V. Seregina, Upper unit of the generalized Pascal pyramid and their interpretations, The Journal of Siberian Federal University, Mathematics and Physics 3(4) (2010), 533-543 (in Russian).
O. V. Kuzmin and M. V. Seregina, Plane sections of the generalized Pascal pyramid and their interpretations, Discrete Math. Appl. 20(4) (2010), 377-389.
O. V. Kuzmin, Generalized Pascal’s pyramids and decision trees, Advances and Applications in Discrete Mathematics 34 (2022), 1-15.
O. V. Kuzmin, A. P. Khomenko and A. I. Artyunin, Discrete model of static loads distribution management on lattice structures, Advances and Applications in Discrete Mathematics 19(3) (2018), 183-193.
O. V. Kuzmin, A. P. Khomenko and A. I. Artyunin, Development of special mathematical software using combinatorial numbers and lattice structure analysis, Advances and Applications in Discrete Mathematics 19(3) (2018), 229-242.
I. G. Macdonald, Symmetric Functions and Hall Polynomials, Second Edition, Clarendon Press, Oxford, 1995, 475 pp.
R. A. Baeza-Yates and B. A. Ribeiro-Neto, Modern Information Retrieval: The Concepts and Technology behind Search (second edition), Addison-Wesley, New York, 2011, 960 pp.
Donald E. Knuth, The Art of Computer Programming, Sorting and Searching. Second Edition, Addison-Wesley, Reading, Massachusetts, 1998, Vol. 3, 780 pp.
C. J. Date, An Introduction to Database Systems, Pearson: Addison-Wesley, Boston, 2004, 983 pp.
Charles T. Meadow, The Analysis of Information Systems, Melville Pub. Co., Los Angeles, 1973, 420 pp.
Gerard Salton, Automatic Information Organization and Retrieval, McGraw-Hill, New York, 1968, 514 pp.
Gerard Salton, Dynamic Information and Library Processing, Prentice-Hall, New York, 1975, 523 pp.
Christopher D. Manning, Prabhakar Raghavan and Hinrich Schutze, Introduction to Information Retrieval, Cambridge University Press, Cambridge, England, 2008, 504 pp.
M. Ushold and M. Gruninger, Ontologies: Principles, Methods and Applications, Knowledge Engineering Review 11(2) (1996), 115-121.
O. V. Kuzmin and T. A. Loginov, Constructing the relevance index with the help of generalized Pascal’s pyramids, The Bulletin of Buryat State University, Series 13: Mathematics and Information Science (3) (2006), 40-45 (in Russian).
M. L. Platonov and V. N. Dokin, Triangular scheme of population evolution, Investigations on Geomagnetics, Aeronomy and Solar Physics, Nauka Publ., Moscow, (35) (1975), 26-31 (in Russian).
O. V. Kuzmin and M. V. Seregina, Upper unit of the generalized Pascal pyramid and their interpretations, Journal of Siberian Federal University, Mathematics and Physics 3(4) (2010), 533-543 (in Russian).
Downloads
Published
Issue
Section
License
Copyright (c) 2024 PUSHPA PUBLISHING HOUSE, PRAYAGRAJ, INDIA
This work is licensed under a Creative Commons Attribution 4.0 International License.
_________________________
Attribution: Credit Pushpa Publishing House as the original publisher, including title and author(s) if applicable.
Contact Pushpa Publishing House for more info or permissions.
Journal Impact Factor: 
