Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classification of the factorial functions of Eulerian binomial and
  Sheffer posets   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 $2^{n-1}$, 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 infinite Boolean algebra with two new
coatoms inserted, or the infinite cubical poset. Moreover, we are able to
classify the Sheffer factorial functions of Eulerian Sheffer posets with
binomial factorial function $B(n) = 2^{n-1}$ as the doubling of an upside down
tree with ranks 1 and 2 modified.
  When we impose the further condition that a given Eulerian binomial or
Eulerian Sheffer poset is a lattice, this forces the poset to be the infinite
Boolean algebra $B_X$ or the infinite cubical lattice $C_X^{< \infty}$. We also
include several poset constructions that have the same factorial functions as
the infinite cubical poset, demonstrating that classifying Eulerian Sheffer
posets is a difficult problem.

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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: funct-an
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The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-th