Block intersection polynomials

Peter J. Cameron; Leonard H. Soicher

doi:10.1112/blms/bdm034

Block intersection polynomials

Peter J. Cameron, Leonard H. Soicher

Centre for Interdisciplinary Research in Computational Algebra

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	559-564
Number of pages	6
Journal	Bulletin of the London Mathematical Society
Volume	39
Issue number	4
DOIs	https://doi.org/10.1112/blms/bdm034
Publication status	Published - 1 Jan 2007

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title = "Block intersection polynomials",

abstract = "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.",

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AU - Soicher, Leonard H.

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AB - 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.

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DO - 10.1112/blms/bdm034

M3 - Article

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SN - 0024-6093

VL - 39

SP - 559

EP - 564

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

IS - 4

ER -

Block intersection polynomials

Abstract

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