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Paper   IPM / M / 15689
School of Mathematics
  Title:   Decomposable clutters and a generalization of Simon's conjecture
  Author(s):  Mina Bigdeli (Joint with A. A. Yazdan Pour and R. Zaare-Nahandi)
  Status:   Published
  Journal: J. Algebra
  Vol.:  531
  Year:  2019
  Pages:   102-124
  Supported by:  IPM
Each (equigenerated) squarefree monomial ideal in the polynomial ring S=K[x_1,…,x_n ] represents a family of subsets of [n], called a (uniform) clutter. In this paper, we introduce a class of uniform clutters, called decomposable clutters, whose associated ideal has linear quotients and hence linear resolution over all fields. We show that chordality of these clutters guarantees the correctness of a conjecture raised by R. S. Simon on extendable shellability of d-skeletons of a simplex 〈[n]〉 for all d. We then prove this conjecture for d≥n-3.

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