Classification of the factorial functions of Eulerian binomial and Sheffer posets

@article{Ehrenborg2007ClassificationOT,
  title={Classification of the factorial functions of Eulerian binomial and Sheffer posets},
  author={Richard Ehrenborg and Margaret Readdy},
  journal={J. Comb. Theory, Ser. A},
  year={2007},
  volume={114},
  pages={339-359}
}
We give a complete classification of the factorial functions of Eulerian binomial posets. The factorial function B(n) either coincides with n!, the factorial function of the infinite Boolean algebra, or 2n−1, the factorial function of the infinite butterfly poset. We also classify the factorial functions for Eulerian Sheffer posets. An Eulerian Sheffer poset with binomial factorial function B(n) = n! has Sheffer factorial function D(n) identical to that of the infinite Boolean algebra, the… CONTINUE READING