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A note on λ ‐designs
Author(s) -
Yadav Ajeet K.,
Pawale Rajendra M.,
Shrikhande Mohan S.
Publication year - 2020
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.21752
Subject(s) - mathematics , prime (order theory) , type (biology) , combinatorics , prime power , block (permutation group theory) , arithmetic , discrete mathematics , ecology , biology
Let r and r′ , ( r > r′ ) be the two replication numbers of a λ ‐design D . We show that if r − r ′ is a prime power or 33, then D is a design of type‐1. We derive two inequalities, where equality holds if and only if D is a design of type‐1. Let D be a λ ‐design with two block sizes with v = n p + 1 points, where p is prime and 2 ⩽ n ⩽ 22 . We develop a procedure to obtain exceptions for such type‐1 λ ‐designs, refining earlier results.