• Corpus ID: 251765453

# Maximal degree subposets of $\nu$-Tamari lattices

@inproceedings{Dermenjian2022MaximalDS,
title={Maximal degree subposets of \$\nu\$-Tamari lattices},
author={Aram Dermenjian},
year={2022}
}
. In this paper, we study two diﬀerent subposets of the ν -Tamari lattice: one in which all elements have maximal in-degree and one in which all elements have maximal out-degree. The maximal in-degree and maximal out-degree of a ν -Dyck path turns out to be the size of the maximal staircase shape path that ﬁts weakly above ν . For m -Dyck paths of height n , we further show that the maximal out-degree poset is poset isomorphic to the ν -Tamari lattice of ( m − 1)-Dyck paths of height n , and…

## References

SHOWING 1-10 OF 14 REFERENCES

• Mathematics
Electron. J. Comb.
• 2020
It is shown that the ν-Tamari is isomorphic to the increasing-flip poset of a suitably chosen subword complex, and settle a special case of Rubey’s lattice conjecture concerning thePoset of pipe dreams defined by chute moves.
• Mathematics
• 2021
We present a unifying framework in which both the ν-Tamari lattice, introduced by Préville-Ratelle and Viennot, and principal order ideals in Young’s lattice indexed by lattice paths ν, are realized
• Mathematics
Transactions of the American Mathematical Society
• 2018
In this paper, we exploit the combinatorics and geometry of triangulations of products of simplices to derive new results in the context of Catalan combinatorics of $\nu$-Tamari lattices. In our
• Mathematics
Electron. J. Comb.
• 2011
The number of intervals in this lattice is proved to be  m+1}{n(mn+1)} {(m+1)^2 n+m\choose n-1}.
This paper's aim is to present recent combinatorial considerations on r-Dyck paths, r-Parking functions, and the r-Tamari lattices. Giving a better understanding of the combinatorics of these objects
• Mathematics
• 2011
We consider the graded $\S_n$-modules of higher diagonally harmonic polynomials in three sets of variables (the trivariate case), and show that they have interesting ties with generalizations of the
We introduce and study a new partial order on Dyck paths. We prove that these posets are meet-semilattices. We show that their numbers of intervals are the same as the number of bicubic planar maps.
We enumerate the intervals in the Tamari lattices. For this, we introduce an inductive description of the intervals. Then a notion of "new interval" is defined and these are also enumerated. A a side
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