[PDF][PDF] Cataland: why the fuss?
The main objects of noncrossing Catalan combinatorics associated to a finite Coxeter
system are noncross-ing partitions, sortable elements, and cluster complexes. The first and …
system are noncross-ing partitions, sortable elements, and cluster complexes. The first and …
Generalized -Catalan numbers
Recent work of the first author, Negut, and Rasmussen, and of Oblomkov and Rozansky in
the context of Khovanov–Rozansky knot homology produces a family of polynomials in q …
the context of Khovanov–Rozansky knot homology produces a family of polynomials in q …
[HTML][HTML] Cores with distinct parts and bigraded Fibonacci numbers
K Paramonov - Discrete Mathematics, 2018 - Elsevier
The notion of (a, b)-cores is closely related to rational (a, b)-Dyck paths via the bijection due
to J. Anderson, and thus the number of (a, a+ 1)-cores is given by the Catalan number C a …
to J. Anderson, and thus the number of (a, a+ 1)-cores is given by the Catalan number C a …
Higher rank -Catalan polynomials, affine Springer fibers, and a finite Rational Shuffle Theorem
N González, J Simental, M Vazirani - arXiv preprint arXiv:2303.15694, 2023 - arxiv.org
We introduce the higher rank $(q, t) $-Catalan polynomials and prove they equal truncations
of the Hikita polynomial to a finite number of variables. Using affine compositions and a …
of the Hikita polynomial to a finite number of variables. Using affine compositions and a …
Higher rank (𝑞, 𝑡)-Catalan polynomials, affine Springer fibers, and a finite rational shuffle theorem
N González, J Simental, M Vazirani - Transactions of the American …, 2024 - ams.org
We introduce the higher rank $(q, t) $-Catalan polynomials and prove they equal truncations
of the Hikita polynomial to a finite number of variables. Using affine compositions and a …
of the Hikita polynomial to a finite number of variables. Using affine compositions and a …
Some natural extensions of the parking space
M Konvalinka, V Tewari - Journal of Combinatorial Theory, Series A, 2021 - Elsevier
We construct a family of S n modules indexed by c∈{1,…, n} with the property that upon
restriction to S n− 1 they recover the classical parking function representation of Haiman …
restriction to S n− 1 they recover the classical parking function representation of Haiman …
The combinatorics of knot invariants arising from the study of Macdonald polynomials
J Haglund - Recent trends in combinatorics, 2016 - Springer
This chapter gives an expository account of some unexpected connections which have
arisen over the last few years between Macdonald polynomials, invariants of torus knots …
arisen over the last few years between Macdonald polynomials, invariants of torus knots …
Advances in the theory of cores and simultaneous core partitions
R Nath - The American Mathematical Monthly, 2017 - Taylor & Francis
The theory of s-core partitions, integer partitions whose hook sets avoid hooks of length s,
lies at the intersection of a surprising number of fields, including number theory …
lies at the intersection of a surprising number of fields, including number theory …
[PDF][PDF] ALGEBRAIC COMBINATORICS
Recent work of the first author, Negut, and Rasmussen, and of Oblomkov and Rozansky in
the context of Khovanov–Rozansky knot homology produces a family of polynomials in q …
the context of Khovanov–Rozansky knot homology produces a family of polynomials in q …
[PDF][PDF] Representation Theory Connections to (q, t)-Combinatorics 19w5131
F Bergeron, J Haglund, M Zabrocki - 2019 - birs.ca
• In 1988, Macdonald [Mac88] introduced a family of symmetric functions Pλ (X; q, t) that
depended on parameters q and t and a family of non-symmetric polynomials Eα (X; q, t) …
depended on parameters q and t and a family of non-symmetric polynomials Eα (X; q, t) …