Abstract
A new method to study families of finite sets, in particular t-designs, by studying families of multisets (also called lists) and their relationships with families of sets, is developed. Notion of the tag for a subset defined earlier by one of the authors is extended to a submultiset. A new concept t-(v, k, λ) list design is defined and studied. Basic existence theory for designs is extended to a new set up of list designs. In particular tags are used to prove that signed t-list designs exist whenever necessary conditions are satisfied. The concepts of homomorphisms and block spreading are extended to this new set up.
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This is one of several papers published together in Designs, Codes and Cryptography on the special topic: “Combinatorics – A Special Issue Dedicated to the 65th Birthday of Richard Wilson”.
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Singhi, N., Ray-Chaudhuri, D.K. Studying designs via multisets. Des. Codes Cryptogr. 65, 365–381 (2012). https://doi.org/10.1007/s10623-012-9708-0
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DOI: https://doi.org/10.1007/s10623-012-9708-0