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Intersecting Chains in Finite Vector Spaces

1999
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Combinatorics, probability & computing
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We prove an Erdős-Ko-Rado-type theorem for intersecting k-chains of subspaces of a finite vector space. This is the q-generalization of earlier results of Erdős, Seress and Székely for intersecting k-chains of subsets of an underlying set. The proof hinges on the author's proper generalization of the shift technique from extremal set theory to finite vector spaces, which uses a linear map to define the generalized shift operation. The theorem is the following. For c = 0, 1, consider k-chains of

doi:10.1017/s0963548399004010
fatcat:ueg6dfgjrzdbvknaybhl2zawyu