多重集合
出典と参考文献

1 2 3  Knuth, Donald E. (1998). The Art of Computer Programming – Vol. 2: Seminumerical Algorithms (3rd edition ed.). Addison Wesley. pp. 694. ISBN 0201896842  

クヌースは同書で、多重集合に対して提案された他の名前（例えば,リスト(list)、まとまり(bunch)、バッグ(bag)、堆積(heap)、標本(sample)、重みつき集合(weighted set)、コレクション(collection)、組(suite).など）も提示している。
1 2  
Wayne D. Blizard (1991). “The development of multiset theory”. The Review of Modern Logic 1 (4):  319-352. https://projecteuclid.org/journals/modern-logic/volume-1/issue-4/The-development-of-multiset-theory/rml/1204834739.full 2022年2月12日閲覧。. 

多重集合の歴史に関するサーベイ論文である。
↑  デーデキント; 河野伊三郎 (訳) (1967). 数について. 岩波書店. pp. 139. ISBN 4003392418
↑  
Syropoulos, Apostolos (2001). C. S. Calude et al.. ed. “Mathematics of Multisets” (PDF). WMP '00 Proceedings of the Workshop on Multiset Processing: Mathematical, Multiset Processing, Mathematical, Computer Science, and Molecular Computing Points of View (Springer-Verlag):  347–358. ISBN 3-540-43063-6. http://citeseerx.ksu.edu.sa/viewdoc/summary?doi=10.1.1.58.5406 2010年11月26日閲覧。.
↑  Hein, James L. (2003). Discrete mathematics. Jones & Bartlett Publishers. pp. 29–30. ISBN 0-7637-2210-3
↑  Cristian S. Calude, Gheorghe Păun, Grzegorz Rozenberg, Arto Salomaa, Multiset Processing: Mathematical, Computer Science, and Molecular Computing Points of View Springer Verlag 2001, ISBN 3-540-43063-6 S. 105
↑  Blizard, Wayne D (1989). “Multiset theory”. Notre Dame Journal of Formal Logic 30 (1):  36–66. doi:10.1305/ndjfl/1093634995. http://projecteuclid.org/download/pdf_1/euclid.ndjfl/1093634995.
1 2 3  Blizard, Wayne D. (1991). “The Development of Multiset Theory”. Modern Logic 1 (4):  319–352. http://projecteuclid.org/download/pdf_1/euclid.rml/1204834739.
↑  Peterson, James L. (1981). Petri Net Theory and the Modelling of Systems. Englewood Cliffs, New Jersey: Prentice-Hall. http://jklp.org/profession/books/pn/
↑  Cerf, Vint; Fernandez, E.; Gostelow, K.; Volansky, S. (December 1971). Formal Control Flow Properties of a Model of Computation (Report). Los Angeles, California: Computer Science Department, University of California. ENG-7178。
1 2  Singh, D.; Ibrahim, A. M.; Yohanna, T.; Singh, J. N. (2007). “An overview of the applications of multisets”. Novi Sad Journal of Mathematics 37 (2):  73–92.
↑  Angelelli, I. (1965). “Leibniz's misunderstanding of Nizolius' notion of 'multitudo'”. Notre Dame Journal of Formal Logic (6):  319–322.
↑  Kircher, Athanasius (1650). Musurgia Universalis. Rome: Corbelletti
↑  Prestet, Jean (1675). Elemens des Mathematiques. Paris: André Pralard
↑  Wallis, John (1685). A treatise of algebra. London: John Playford
↑  Dedekind, Richard (1888). Was sind und was sollen die Zahlen?. Braunschweig: Vieweg
↑  Syropoulos, Apostolos (2001). “Mathematics of Multisets”. In Calude, C. S.. Multiset processing: Mathematical, computer science, and molecular computing points of view. Springer-Verlag. pp. 347–358
↑  例えばStanley 1997
↑  Weisstein, Eric W. "Multichoose". mathworld.wolfram.com (英語).
↑  Aigner, M. (1979). Combinatorial Theory. New York/Berlin: Springer Verlag
↑  Anderson, I. (1987). Combinatorics of Finite Sets. Oxford: Clarendon Press
↑  Stanley, Richard P. (1997). Enumerative Combinatorics. 1. Cambridge University Press. ISBN 0-521-55309-1. http://www-math.mit.edu/~rstan/ec/
↑  Stanley, Richard P. (1999). Enumerative Combinatorics. 2. Cambridge University Press. ISBN 0-521-56069-1
↑  Grumbach, S.; Milo, T (1996). “Towards tractable algebras for bags”. Journal of Computer and System Sciences 52 (3):  570–588.
↑  Libkin, L.; Wong, L. (1994). “Some properties of query languages for bags”. Proceedings of the Workshop on Database Programming Languages. Springer Verlag. pp. 97–114
↑  Libkin, L.; Wong, L. (1995). “On representation and querying incomplete information in databases with bags”. Information Processing Letters 56 (4):  209–214.
↑  Yager, R. R. (1986). “On the Theory of Bags”. International Journal of General Systems 13:  23–37.
↑  Grzymala-Busse, J. (1987). “Learning from examples based on rough multisets”. Proceedings of the 2nd International Symposium on Methodologies for Intelligent Systems. Charlotte, North Carolina. pp. 325–332
↑  Blizard, Wayne D. (1989). “Real-valued Multisets and Fuzzy Sets”. Fuzzy Sets and Systems 33:  77–97.
↑  Blizard, Wayne D. (1990). “Negative Membership”. Notre Dame Journal of Formal Logic 31 (1):  346–368.
↑  Loeb, D. (1992). “Sets with a negative numbers of elements”. Advances in Mathematics 91:  64–74.
↑  Miyamoto, S. (2001). “Fuzzy Multisets and their Generalizations”. Multiset Processing 2235:  225–235.
↑  Alkhazaleh, S.; Salleh, A. R.; Hassan, N. (2011). “Soft Multisets Theory”. Applied Mathematical Sciences 5 (72):  3561–3573.
↑  Alkhazaleh, S.; Salleh, A. R. (2012). “Fuzzy Soft Multiset Theory”. Abstract and Applied Analysis.
↑  Burgin, Mark (1990). “Theory of Named Sets as a Foundational Basis for Mathematics”. Structures in Mathematical Theories. San Sebastian. pp. 417–420. http://www.blogg.org/blog-30140-date-2005-10-26.html
↑  Burgin, Mark (1992). “On the concept of a multiset in cybernetics”. Cybernetics and System Analysis 3:  165–167.
↑  Burgin, Mark (2004). "Unified Foundations of Mathematics". arXiv:math/0403186。
↑  Burgin, Mark (2011). Theory of Named Sets. Mathematics Research Developments. Nova Science Pub Inc. ISBN 978-1-61122-788-8