• 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… 

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References

SHOWING 1-10 OF 14 REFERENCES

The ν-Tamari Lattice via ν-Trees, ν-Bracket Vectors, and Subword Complexes

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.

A unifying framework for the $\nu$-Tamari lattice and principal order ideals in Young's lattice

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

Geometry of $\nu $-Tamari lattices in types $A$ and $B$

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

The Number of Intervals in the m-Tamari Lattices

The number of intervals in this lattice is proved to be $$ m+1}{n(mn+1)} {(m+1)^2 n+m\choose n-1}.

The enumeration of generalized Tamari intervals

Combinatorics of r-Dyck paths, r-Parking functions, and the r-Tamari lattices

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

Higher Trivariate Diagonal Harmonics via generalized Tamari Posets

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

Some properties of a new partial order on Dyck paths

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.

Sur le nombre d'intervalles dans les treillis de Tamari

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

Monoïdes préordonnés et chaînes de Malcev

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