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Let L be a finite geometric lattice of rank r, and for i =0, I, • • • » r, let W. denote the number of elements of L with rank i. 12 fe r—k r—l r—1 with equality if and only if the lattice L is modular. We give two further results concerning matchings of lattice elements of rank < k into those of rank > r — k, and observe that a middle term can be… (More)

- Thomas A. Dowling
- J. Comb. Theory, Ser. B
- 1977

ACKNOWLEDGEMENTS To the members of the faculty of the Department of Statistics who have contributed to my graduate training I wish to express my sincere gratitude. Special thanks are owed to my advisor, Professor R. C. Bose, for his guidance and encouragement during my research and for his stimulating lectures which first aroused my interest in… (More)

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