[HTML][HTML] Refined knot invariants and Hilbert schemes
E Gorsky, A Neguţ - Journal de mathématiques pures et appliquées, 2015 - Elsevier
We consider the construction of refined Chern–Simons torus knot invariants by M. Aganagic
and S. Shakirov from the DAHA viewpoint of I. Cherednik. We give a proof of Cherednik's …
and S. Shakirov from the DAHA viewpoint of I. Cherednik. We give a proof of Cherednik's …
[HTML][HTML] The representation of the symmetric group on m-Tamari intervals
M Bousquet-Mélou, G Chapuy… - Advances in …, 2013 - Elsevier
An m-ballot path of size n is a path on the square grid consisting of north and east unit steps,
starting at (0, 0), ending at (mn, n), and never going below the line {x= my}. The set of these …
starting at (0, 0), ending at (mn, n), and never going below the line {x= my}. The set of these …
The polytope of Tesler matrices
K Mészáros, AH Morales, B Rhoades - Selecta Mathematica, 2017 - Springer
We introduce the Tesler polytope Tes _n (a) Tes n (a), whose integer points are the Tesler
matrices of size n with hook sums a_1, a_2, ..., a_n ∈ Z _ ≥ 0 a 1, a 2,…, an∈ Z≥ 0. We …
matrices of size n with hook sums a_1, a_2, ..., a_n ∈ Z _ ≥ 0 a 1, a 2,…, an∈ Z≥ 0. We …
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 …
A weighted sum over generalized Tesler matrices
AT Wilson - Journal of Algebraic Combinatorics, 2017 - Springer
We generalize previous definitions of Tesler matrices to allow negative matrix entries and
negative hook sums. Our main result is an algebraic interpretation of a certain weighted sum …
negative hook sums. Our main result is an algebraic interpretation of a certain weighted sum …
Capacity bounds on integral flows and the Kostant partition function
J Leake, AH Morales - arXiv preprint arXiv:2406.07838, 2024 - arxiv.org
The type $ A $ Kostant partition function is an important combinatorial object with various
applications: it counts integer flows on the complete directed graph, computes Hilbert series …
applications: it counts integer flows on the complete directed graph, computes Hilbert series …
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 …
Flow polytopes and the space of diagonal harmonics
RI Liu, AH Morales, K Mészáros - Canadian Journal of Mathematics, 2019 - cambridge.org
Flow Polytopes and the Space of Diagonal Harmonics Page 1 http://dx.doi.org/. /CJM-- ©Canadian
Mathematical Society Flow Polytopes and the Space of Diagonal Harmonics Ricky Ini Liu …
Mathematical Society Flow Polytopes and the Space of Diagonal Harmonics Ricky Ini Liu …
Parking functions, Shi arrangements, and mixed graphs
The Shi arrangement is the set of all hyperplanes in ℝ n of the form xj− xk= 0 or 1 for 1≤ j<
k≤ n. Shi observed in 1986 that the number of regions (ie, connected components of the …
k≤ n. Shi observed in 1986 that the number of regions (ie, connected components of the …
Kostant's partition function and magic multiplex juggling sequences
Kostant's partition function is a vector partition function that counts the number of ways one
can express a weight of a Lie algebra gg as a nonnegative integral linear combination of the …
can express a weight of a Lie algebra gg as a nonnegative integral linear combination of the …