Erdős-Ko-Rado and Hilton-Milner type theorems for intersecting chains in posets

Erdős, Péter and Seress, Ákos and Székely, Á. László (2000) Erdős-Ko-Rado and Hilton-Milner type theorems for intersecting chains in posets. COMBINATORICA, 20 (1). pp. 27-45. ISSN 0209-9683

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Abstract

We prove Erdos-Ko-Rado and Hilton-Milner type theorems for t-intersecting k-chains in posets using the kernel method. These results are common generalizations of the original EKR and HM theorems, and our earlier results for intersecting k-chains in the Boolean algebra. For intersecting k-chains in the c-truncated Boolean algebra we also prove an exact EKR type theorem (for all n) using the shift method. An application of the general theorem gives a similar result for t-intersecting chains if n is large enough.

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