2 citations · 6 across the 8 of their papers we have counts for
10 papers
Bicolored Eulerian quasisymmetric functions, affine lengths, and Theta operators
Hsin-Chieh Liao, Hai Zhu
We introduce a -analogue of the bicolored Eulerian quasisymmetric functions by incorporating an additional grading arising from affine length, obtained by interpreting bicolored…
Restrictions of the dot action representation
Hsin-Chieh Liao, Martha Precup, John Shareshian
Regular semisimple Hessenberg varieties are subvarieties of flag varieties defined for any reductive group. Their cohomology carries a representation of the associated Weyl group,…
Equivariant gamma-positivity of matroid Chow rings
Hsin-Chieh Liao
In this paper, we prove that the Chow ring and augmented Chow ring of a matroid are equivariantly -positive under the action of any group of automorphisms. Our approach provides…
Chow rings and augmented Chow rings of uniform matroids and their -analogs
Hsin-Chieh Liao
We study the Hilbert series and the representations of and on the (augmented) Chow rings of uniform matroids and -uniform matroid…
Stembridge codes, permutahedral varieties, and their extensions
Hsin-Chieh Liao
It is well known that the Eulerian polynomial is the Hilbert series of the cohomology of the permutahedral variety. Stanley obtained a formula showing that the cohomology carries a…
Combinatorics of generalized parking-function polytopes
Margaret M. Bayer, Steffen Borgwardt, Teressa Chambers +8
For , a -parking function is defined to be a sequence of positive integers whose nondecreasing rearra…
Stembridge codes and Chow rings
Hsin-Chieh Liao
It is well known that the Eulerian polynomial is the Hilbert series of the cohomology of the permutohedral variety. We answer a question of Stembridge on finding a geometric explan…
Revisiting the general cubic: A simplification of Cardano's solution
Hsin-Chieh Liao, Peter Jao-Shyong Shiue, Mark Saul
Motivated by the recent work of William Y.C. Chen, in which he presents a way to solve cubic equations by considering the identity of Sylvester, we investigate the solutions obtain…
Folding Phenomenon of Major-balance Identities on Restricted Involutions
Tung-Shan Fu, Hsian-Chun Hsu, Hsin-Chieh Liao
In this paper we prove a refined major-balance identity on the -avoiding involutions of length , respecting the leading element of permutations. The proof is based on a sig…
Signed Countings of types B and D permutations and -Euler Numbers
Sen-Peng Eu, Tung-Shan Fu, Hsiang-Chun Hsu +1
It is a classical result that the parity-balance of the number of weak excedances of all permutations (derangements, respectively) of length is the Euler number , alternat…