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1 thg 10, 2003 · Briefly, a nested triple system on a set S can be defined as a set, t, of 4-subsets of S where the six edges of each 4-subset are partitioned into a triangle and a star K1,3, in such a way that every pair of S occurs exactly once in a triangle and once in a star.
21 thg 10, 2024 · For a given SQS and a nested quadruple system for it, the number of times (multiplicity) that each pair is contained in this partition is considered. A pair which is contained in the partition of some block will be called a nested design pair(in short, ND-pair) .
20 thg 2, 2025 · Motivated by a repair problem for fractional repetition codes in distributed storage, each block of any Steiner quadruple system (SQS) of order $v$ is partitioned into two pairs.
Abstract:Motivated by a repair problem for fractional repetition codes in distributed storage, each block of any Steiner quadruple system (SQS) of order $v$ is partitioned into two pairs.
5 thg 5, 2021 · Section 3 gives a doubling construction of doubly resolvable Steiner quadruple systems. We define doubly resolvable pair of matching partial candelabra quadruple systems and give a construction in Sect. 4.
Motivated by a repair problem for fractional repetition codes in distributed storage, each block of any Steiner quadruple system (SQS) of order $v$ is partitioned into two pairs.
18 thg 10, 2024 · Motivated by a repair problem for fractional repetition codes in distributed storage, each block of any Steiner quadruple system (SQS) of order $v$ is partitioned into two pairs.
October 21, 2024 Abstract der v is partitioned into two pairs. Each pair in such a partition is called a nested design pair and its multiplicity is the number of imes it is a pair in this partition. Such a partition of each block is considered as a new block design call
28 thg 8, 2025 · A Steiner quadruple system is a Steiner system S (t=3,k=4,v), where S is a v-set and B is a collection of k-sets of S such that every t-subset of S is contained in exactly one member of B. Barrau (1908) established the uniqueness of S (3,4,8), 1 2 4 8; 2 3 5 8; 3 4 6 8; 4 5 7 8; 1 5 6 8; 2 6 7 8; 1 3 7 8 3 5 6 7; 1 4 6 7; 1 2 5 7; 1 2 3 6; 2 3 ...
27 thg 2, 2025 · Of special interest are nested quadruple systems in which all the pairs are nested design pairs with the same multiplicity. Several constructions of nested quadruple systems are considered, and in particular, classic constructions of SQS are examined.
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