# Rational Dyck paths and decompositions

@inproceedings{Shigechi2021RationalDP, title={Rational Dyck paths and decompositions}, author={Keiichi Shigechi}, year={2021} }

We study combinatorial properties of a rational Dyck path by decomposing it into a tuple of Dyck paths. The combinatorial models such as b-Stirling permutations, (b + 1)-ary trees, parenthesis presentations, and binary trees play central roles to establish a correspondence between the rational Dyck path and the tuple of Dyck paths. We reinterpret two orders, the Young and the rotation orders, on rational Dyck paths in terms of the tuple of Dyck paths by use of the decomposition. As an…

## References

SHOWING 1-10 OF 19 REFERENCES

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

- 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…

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

- MathematicsElectron. 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.

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

- MathematicsTransactions 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…

### Higher Trivariate Diagonal Harmonics via generalized Tamari Posets

- 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…

### The ν-Tamari lattice via ν-trees

- ν-bracket vectors, and subword complexes, preprint
- 2018