Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Eulerian polynomials on segmented permutations   We define a generalization of the Eulerian polynomials and the Eulerian
numbers by considering a descent statistic on segmented permutations coming
from the study of 2-species exclusion processes and a change of basis in a Hopf
algebra. We give some properties satisfied by these generalized Eulerian
numbers. We also define a $q$-analog of these Eulerian polynomials which gives
back usual Eulerian polynomials and ordered Bell polynomials for specific
values of its variables. We also define a noncommutative analog living in the
algebra of segmented compositions. It gives us an explicit generating function
and some identities satisfied by the generalized Eulerian polynomials such as a
Worpitzky-type relation.

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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
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The categories of this paper are: eess
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The categories of this paper are: hep-th
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The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys