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Construction of balanced designs and related identities

Contributed Papers

Part of the Lecture Notes in Mathematics book series (LNM,volume 748)

Abstract

A balanced n-ary design is a design on V elements arranged in B blocks of size K such that each element can occur 0,1,2,..., or n-1 times in each block (so that the blocks are collections of elements rather than subsets) and such that , constant, where nij is the number of times the ith element occurs in the jth block, i=1, ...,V, j=1,...,B. So a balanced binary design is merely a balanced incomplete block design (BIBD).

Any m BIBDs, based on the same set of elements, are used in two constructions to yield balanced (m+1)-ary designs. Some interesting combinatorial identities are involved.

Similar constructions using BIBDs with λ=1 and 2 yield other BIBDs.

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© 1979 Springer-Verlag

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Morgan, E.J. (1979). Construction of balanced designs and related identities. In: Horadam, A.F., Wallis, W.D. (eds) Combinatorial Mathematics VI. Lecture Notes in Mathematics, vol 748. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0102686

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  • DOI: https://doi.org/10.1007/BFb0102686

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09555-2

  • Online ISBN: 978-3-540-34857-3

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