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J. Korean Math. Soc. 2020; 57(6): 1323-1333

Online first article September 21, 2020      Printed November 1, 2020

https://doi.org/10.4134/JKMS.j190161

Copyright © The Korean Mathematical Society.

Erd\H os-Ko-Rado type theorems for simplicial complexes via algebraic shifting

Younjin Kim

Ewha Womans University

Abstract

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In 2009, Borg~\cite{BORG13} suggested a conjecture concerning the size of a $t$-intersecting $k$-uniform family of faces of an arbitrary simplicial complex. In this paper, we give a strengthening of Borg's conjecture for shifted simplicial complexes using algebraic shifting.

Keywords: Erdos-Ko-Rado theorem, simplicial complexes, algebraic shifting

MSC numbers: Primary 05D05, 05E45

Supported by: This work was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2017R1A6A3A04005963)

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