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Characterizing maximal shifted intersecting set systems and short injective proofs of the Erdős–Ko–Rado and Hilton–Milner theorems

Nguyen Trong Tuan and Nguyen Anh Thi

Vol. 12 (2023), No. 1, 89–96
Abstract

We give a canonical partition of shifted intersecting set systems, from which one can obtain unified and elementary proofs of the Erdős–Ko–Rado and Hilton–Milner theorems, as well as a characterization of maximal shifted k-uniform intersecting set systems over a set of n elements.

Keywords
shifted intersecting set systems, $k$-uniform, Erdős–Ko–Rado theorem, Hilton–Milner theorem
Mathematical Subject Classification
Primary: 05D05
Milestones
Received: 24 August 2022
Revised: 7 October 2022
Accepted: 28 October 2022
Published: 29 March 2023
Authors
Nguyen Trong Tuan
Faculty of Mathematics and Computer Science
University of Science
Vietnam National University
Ho Chi Minh City
Vietnam
Nguyen Anh Thi
Faculty of Mathematics and Computer Science
University of Science
Vietnam National University
Ho Chi Minh City
Vietnam