8 papers · 1 filter
Planar networks and total positivity of Riordan arrays
Lanqi Du, Ethan Y. H. Li
In 2015, Chen, Liang and Wang provided several sufficient conditions for the total positivity of Riordan arrays and asked for combinatorial proofs of these results. In this paper,…
A quantitative way to e-positivity of trees
Ethan Y. H. Li
In 2020, Dahlberg, She, and van Willigenburg conjectured that the chromatic symmetric function of any tree with maximum degree at least 4 is not e-positive. Zheng and Tom verified…
A symmetric function approach to log-concavity of independence polynomials
Ethan Y. H. Li, Grace M. X. Li, Arthur L. B. Yang +1
As introduced by Gutman and Harary, the independence polynomial of a graph serves as the generating polynomial of its independent sets. In 1987, Alavi, Malde, Schwenk and Erdős con…
Strongly nice property and Schur positivity of graphs
Ethan Y. H. Li, Grace M. X. Li, Arthur L. B. Yang +1
Motivated by the notion of nice graphs, we introduce the concept of strongly nice property, which can be used to study the Schur positivity of symmetric functions. We show that a g…
Induced log-concavity of equivariant matroid invariants
Alice L. L. Gao, Ethan Y. H. Li, Matthew H. Y. Xie +2
Inspired by the notion of equivariant log-concavity, we introduce the concept of induced log-concavity for a sequence of representations of a finite group. For an equivariant matro…
A planar network proof for Hankel total positivity of type Narayana polynomials
Ethan Y. H. Li, Grace M. X. Li, Arthur L. B. Yang +1
The Hankel matrix of type B Narayana polynomials was proved to be totally positive by Wang and Zhu, and independently by Sokal. Pan and Zeng raised the problem of giving a planar n…
Immanant Positivity for Catalan-Stieltjes Matrices
Ethan Y. H. Li, Grace M. X. Li, Arthur L. B. Yang +1
In this paper we give some sufficient conditions for the nonnegativity of immanants of square submatrices of Catalan-Stieltjes matrices and their corresponding Hankel matrices. To…
The twinning operation on graphs does not always preserve -positivity
Ethan Y. H. Li, Grace M. X. Li, David G. L. Wang +1
Motivated by Stanley's -free conjecture on chromatic symmetric functions, Foley, Hoàng and Merkel introduced the concept of strong -positivity and conjectured th…