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Trac #30683: Nu Tamari
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In [https://arxiv.org/abs/1406.3787] the authors define a new
generalization to the Tamari lattice which they name the `\nu`-Tamari
lattice. These are paths which are weakly above a (fixed given) path
(named `\nu`). This ticket aims to add Nu Dyck Words (paths weakly above
a given path) in addition to the Nu Tamari Lattice.

I wasn't sure if I wanted to incorporate Dyck words and the generalized
Tamari lattice into this or not, so for now I haven't and wanted to get
others' opinions before doing that. In addition, that could be a
separate ticket potentially as a "future" goal.

URL: https://trac.sagemath.org/30683
Reported by: aram.dermenjian
Ticket author(s): Aram Dermenjian
Reviewer(s): Frédéric Chapoton
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Release Manager committed Jun 12, 2022
2 parents 346b3b0 + 8de8827 commit 8dad9ce
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2 changes: 2 additions & 0 deletions src/doc/en/reference/combinat/module_list.rst
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Expand Up @@ -164,6 +164,8 @@ Comprehensive Module List
sage/combinat/ncsym/ncsym
sage/combinat/necklace
sage/combinat/non_decreasing_parking_function
sage/combinat/nu_dyck_word
sage/combinat/nu_tamari_lattice
sage/combinat/ordered_tree
sage/combinat/output
sage/combinat/parallelogram_polyomino
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7 changes: 7 additions & 0 deletions src/doc/en/reference/references/index.rst
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Expand Up @@ -998,6 +998,9 @@ REFERENCES:
lacunas of the Thue-Morse word*, Proc. GASCOM 2008 (June
16-20 2008, Bibbiena, Arezzo-Italia), 53--67.
.. [BMFPR] \M. Bousquet-Melou, E. Fusy, L.-F. Preville Ratelle.
*The number of intervals in the m-Tamari lattices*. :arxiv:`1106.1498`
.. [BMS2006] Bugeaud, Mignotte, and Siksek. "Classical and modular
approaches to exponential Diophantine
equations: I. Fibonacci and Lucas perfect powers." Annals
Expand Down Expand Up @@ -4786,6 +4789,10 @@ REFERENCES:
*PICARO - a block cipher allowing efficient higher-order side-channel
resistance*; in ACNS, (2012), pp. 311-328.
.. [PRV2017] \L.-F. Préville-Ratelle and X. Viennot,
*The enumeration of generalized Tamari intervals*.
Trans. Amer. Math. Soc. 369 (2017), pp 5219--5239
.. [Prototype_pattern] Prototype pattern,
:wikipedia:`Prototype_pattern`
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1 change: 1 addition & 0 deletions src/sage/combinat/all.py
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Expand Up @@ -219,6 +219,7 @@
from .subset import Subsets
from .necklace import Necklaces
lazy_import('sage.combinat.dyck_word', ('DyckWords', 'DyckWord'))
lazy_import('sage.combinat.nu_dyck_word', ('NuDyckWords', 'NuDyckWord'))
from .sloane_functions import sloane
lazy_import('sage.combinat.superpartition', ('SuperPartition',
'SuperPartitions'))
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