Density of $f$-ideals and $f$-ideals in mixed small degrees


  • Huy T`ai H`a
  • Graham Keiper
  • Hasan Mahmood
  • Jonathan L. O'Rourke



A squarefree monomial ideal is called an $f$-ideal if its Stanley–Reisner and facet simplicial complexes have the same $f$-vector. We show that $f$-ideals generated in a fixed degree have asymptotic density zero when the number of variables goes to infinity. We also provide novel algorithms to construct $f$-ideals generated in small degrees.


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How to Cite

H`a, H. T. ., Keiper, G., Mahmood, H., & O’Rourke, J. L. . (2022). Density of $f$-ideals and $f$-ideals in mixed small degrees. MATHEMATICA SCANDINAVICA, 128(1).