Representation of numbers by cascades

Authors:
C. C. Chen and D. E. Daykin

Journal:
Proc. Amer. Math. Soc. **59** (1976), 394-398

MSC:
Primary 05A17

DOI:
https://doi.org/10.1090/S0002-9939-1976-0414385-X

MathSciNet review:
0414385

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Abstract | References | Similar Articles | Additional Information

Abstract: A *cascade* is defined as a sum of binomial coefficients

**[1]**Joseph B. Kruskal,*The number of simplices in a complex*, Mathematical optimization techniques, Univ. of California Press, Berkeley, Calif., 1963, pp. 251–278. MR**0154827****[2]**G. Katona,*A theorem of finite sets*, Theory of graphs (Proc. Colloq., Tihany, 1966) Academic Press, New York, 1968, pp. 187–207. MR**0290982****[3]**D. E. Daykin, Jean Godfrey, and A. J. W. Hilton,*Existence theorems for Sperner families*, J. Combinatorial Theory Ser. A**17**(1974), 245–251. MR**416931**, https://doi.org/10.1016/0097-3165(74)90011-9**[4]**D. E. Daykin,*A simple proof of the Kruskal-Katona theorem*, J. Combinatorial Theory Ser. A**17**(1974), 252–253. MR**416932**, https://doi.org/10.1016/0097-3165(74)90012-0**[5]**-,*Cascade algorithms giving Katona-type inequalities*, Nanta. Math. (to appear).**[6]**-,*The average size set in an antichain*, Nanta. Math. (to appear).

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1976-0414385-X

Article copyright:
© Copyright 1976
American Mathematical Society