LINKING SYSTEMS AND MATROID PENCILS(<Special Issue>the 50th Anniversary of the Operations Research Society of Japan)

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  • Linking systems and matroid pencils

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A matroid pencil is a pair of linking systems having the same ground sets in common. It provides a combinatorial abstraction of matrix pencils. This paper investigates the properties of matroid pencils analogous to the theory of Kronecker canonical form. As an application, we give a simple alternative proof for a theorem of Murota on power products of linking systems.

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