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2016

Proof of bijection for combinatorial number system

Siddique, Abu Bakar, Farid, Saadia, Tahir, Muhammad

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Combinatorial number system represents a non-negative natural numbers as sum of binomial coefficients.

This paper presents an induction proof that there exists unique representation of every non-negative natural number $m$ as sum of $r$ binomial coefficients.

Proof of bijection for combinatorial number system · Around

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Beckenbach, Ed. E. F. (1964), ”Applied Combinatorial Mathematics”, pp.27−30
1964
Earlier work this paper cites.
McCaffrey, James (2004), ”Generating the mth Lexicographical Element of a Mathematical Combination”, Microsoft Developer Network
Original
2004
Earlier work this paper cites.

Similar

Knuth, D. E. (2005), ”Generating All Combinations and Partitions”, The Art of Computer Programming, 4, Fascicle 3, Addison-Wesley, pp. 5−6, ISBN 0-201-85394-9
2005
Cited alongside, same era.
Pascal, Ernesto (1887), ”Giornale di Matematiche”, 25, pp. 45−49
Cited in the paper.

Then

Butler, Jon T., and Tsutomu Sasao. ”Index to constant weight codeword converter.” Reconfigurable Computing: Architectures, Tools and Applications. Springer Berlin Heidelberg, 2011. 193-205
2011
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