On an infinite family of generalized PBIBDs
Daniel Kalmanovich
TL;DR
This paper introduces a broad generalization of PBIBDs by removing the commutativity constraint in association schemes, constructing an infinite family for each prime power q ≡ 1 mod 4.
Contribution
It presents the first infinite family of non-commutative PBIBD generalizations, expanding the theoretical framework of combinatorial design theory.
Findings
Constructed an infinite family of non-commutative PBIBDs
Extended the class of association schemes beyond commutative cases
Provided new examples for combinatorial design applications
Abstract
We consider a generalization of the notion of partially balanced incomplete block designs (PBIBDs), by relaxing the requirement that the underlying association scheme be commutative. An infinite family of such generalizations is constructed, one for each prime power congruent to modulo .
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Taxonomy
Topicsgraph theory and CDMA systems · Melanoma and MAPK Pathways