Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Admissible submonoids of Artin-Tits monoids   We show the analogue of Muhlherr's [Coxeter groups in Coxeter groups, Finite
Geom. and Combinatorics, Cambridge Univ. Press (1993), 277-287] for Artin-Tits
monoids, and for Artin-Tits groups of spherical type. That is, the submonoid
(resp. subgroup) of an Artin-Tits monoid (resp. group of spherical type)
induced by an admissible partition of the Coxeter graph is an Artin-Tits monoid
(resp. group). This generalizes and unifies the situation of the submonoid
(resp. subgroup) of fixed elements of an Artin-Tits monoid (resp. group of
spherical type) under the action of graph automorphisms, and the notion of
LCM-homomorphisms defined by Crisp in [Injective maps between Artin groups,
Geom. Group Theory Down Under, Canberra (1996) 119-137] and generalized by
Godelle in [Morphismes injectifs entre groupes d'Artin-Tits, Algebr. Geom.
Topol. 2 (2002), 519--536]. We then complete the classification of the
admissible partitions for which the Coxeter graphs involved have no infinite
label, started by Muhlherr in [Some contributions to the theory of buildings
based on the gate property, Dissertation, T\"ubingen (1994)]. This leads us to
the classification of Crisp's LCM-homomorphisms.

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The categories of this paper are: acc-phys
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The categories of this paper are: hep-th
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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: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
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The categories of this paper are: physics
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The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph