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Article overview
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2-LC triangulated manifolds are exponentially many | Bruno Benedetti
; Marta Pavelka
; | Date: |
23 Jun 2021 | Abstract: | We introduce ’’$t$-LC triangulated manifolds’’ as those triangulations
obtainable from a tree of $d$-simplices by recursively identifying two boundary
$(d-1)$-faces whose intersection has dimension at least $d-t-1$. The $t$-LC
notion interpolates between the class of LC manifolds introduced by
Durhuus-Jonsson (corresponding to the case $t=1$), and the class of all
manifolds (case $t=d$). Benedetti--Ziegler proved that there are at most
$2^{d^2 , N}$ triangulated $1$-LC $d$-manifolds with $N$ facets. Here we prove
that there are at most $2^{frac{d^3}{2}N}$ triangulated $2$-LC $d$-manifolds
with $N$ facets. This extends to all dimensions an intuition by Mogami for
$d=3$. | Source: | arXiv, 2106.12136 | Services: | Forum | Review | PDF | Favorites |
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