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Abstract We study the indexing systems that correspond to equivariant Steiner and linear isometries operads. When G is a finite abelian group, we prove that a G -indexing system is realized by a Steiner operad if and only if it is generated by cyclic G -orbits. When G is a finite cyclic group, whose order is either a prime power or a product of two distinct primes greater than 3, we prove that a G -indexing system is realized by a linear isometries operad if and only if it satisfies Blumberg and Hill’s horn-filling condition. We also repackage the data in an indexing system as a certain kind of partial order. We call these posets transfer systems, and develop basic tools for computing with them.
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On the maximum double independence number of Steiner triple systems
Abstract The maximum independence number of Steiner triple systems of order is well‐known. Motivated by questions of access balancing in storage systems, we determine the maximum total cardinality of a pair of disjoint independent sets of Steiner triple systems of order for all admissible orders.
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- Award ID(s):
- 1814298
- PAR ID:
- 10456668
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Journal of Combinatorial Designs
- Volume:
- 28
- Issue:
- 10
- ISSN:
- 1063-8539
- Format(s):
- Medium: X Size: p. 713-723
- Size(s):
- p. 713-723
- Sponsoring Org:
- National Science Foundation
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