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Block intersection polynomials
Author(s) -
Cameron Peter J.,
Soicher Leonard H.
Publication year - 2007
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdm034
Subject(s) - mathematics , intersection (aeronautics) , block (permutation group theory) , multiplicity (mathematics) , combinatorics , bounding overwatch , discrete mathematics , point (geometry) , computer science , geometry , artificial intelligence , engineering , aerospace engineering
We introduce the block intersection polynomial, which is constructed using certain information about a block design with respect to a subset S of its point‐set, and then provides further information about the number of blocks intersecting S in exactly i points, for i = 0, …, | S |. We also discuss some applications of block intersection polynomials, including bounding the multiplicity of a block in a t ‐( v , k , λ) design and in a resolvable t ‐( v , k , λ) design.