Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ERDŐS-KO-RADO TYPE THEOREMS FOR SIMPLICIAL COMPLEXES VIA ALGEBRAIC SHIFTING

  • Kim, Younjin (Institute of Mathematical Sciences Ewha Womans University)
  • Received : 2019.02.21
  • Accepted : 2020.07.17
  • Published : 2020.11.01
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Abstract

In 2009, Borg [2] 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.

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References

  1. N. Alon, H. Aydinian, and H. Huang, Maximizing the number of nonnegative sub- sets, SIAM J. Discrete Math. 28 (2014), no. 2, 811-816. https://doi.org/10.1137/130947295
  2. P. Borg, Extremal t-intersecting sub-families of hereditary families, J. Lond. Math. Soc. (2) 79 (2009), no. 1, 167-185. https://doi.org/10.1112/jlms/jdn062
  3. P. Erdos, C. Ko, and R. Rado, Intersection theorems for systems of finite sets, Quart. J. Math. Oxford Ser. (2) 12 (1961), 313-320. https://doi.org/10.1093/qmath/12.1.313
  4. S. A. S. Fakhari, Intersecting faces of a simplicial complex via algebraic shifting, Discrete Math. 339 (2016), no. 1, 78-83. https://doi.org/10.1016/j.disc.2015.07.014
  5. P. Frankl, The Erdos-Ko-Rado theorem is true for n = ckt, in Combinatorics (Proc. Fifth Hungarian Colloq., Keszthely, 1976), Vol. I, 365-375, Colloq. Math. Soc. Janos Bolyai, 18, North-Holland, Amsterdam, 1978.
  6. G. Kalai, Algebraic shifting, in Computational commutative algebra and combinatorics (Osaka, 1999), 121-163, Adv. Stud. Pure Math., 33, Math. Soc. Japan, Tokyo, 2002. https://doi.org/10.2969/aspm/03310121
  7. D. Y. Kang, J. Kim, and Y. Kim, On the Erdos-Ko-Rado theorem and the Bollobas theorem for t-intersecting families, European J. Combin. 47 (2015), 68-74. https://doi.org/10.1016/j.ejc.2015.01.009
  8. E. Nevo, Algebraic shifting and basic constructions on simplicial complexes, J. Algebraic Combin. 22 (2005), no. 4, 411-433. https://doi.org/10.1007/s10801-005-4626-0
  9. R. M. Wilson, The exact bound in the Erdos-Ko-Rado theorem, Combinatorica 4 (1984), no. 2-3, 247-257. https://doi.org/10.1007/BF02579226
  10. R. Woodroofe, Erdos-Ko-Rado theorems for simplicial complexes, J. Combin. Theory Ser. A 118 (2011), no. 4, 1218-1227. https://doi.org/10.1016/j.jcta.2010.11.022