Author

Matthew H. Y. Xie

3 papers indexed here

We haven’t gathered this author’s papers yet. Follow them and we’ll fetch their work.

Not the right person? Other researchers publish under this name.

Preprint Oct 2026

A unified approach to infinite log-concavity of combinatorial sequences

We establish a sufficient condition for infinite log-concavity and apply it to five families of combinatorial sequences. We give a new proof of infinite log-concavity for the Boros--Moll coefficient sequences $(d_k(n))_{k=0}^n$ for fixed $n$. For the transposed sequences $(d_\ell(\ell+k))_{k\ge0}$, we prove Zhao's conj...

Matthew H. Y. Xie, Candice X. T. Zhang, Philip B. Zhang · 0 citations

Preprint Sep 2026

Real-rootedness of the $Z$-polynomials of sparse paving matroids and strict interlacing for uniform matroids

We prove that the $Z$-polynomial of every sparse paving matroid has only negative real zeros, confirming the real-rootedness conjecture of Proudfoot, Xu, and Young for this class. We also prove that, for each fixed positive corank, the $Z$-polynomials of uniform matroids in consecutive ranks strictly interlace. Our app...

Matthew H. Y. Xie, Philip B. Zhang · 1 citation

Preprint Sep 2026

Infinite log-concavity of the Boros--Moll sequences

Let $(d_i(n))_{i=0}^n$ be the Boros--Moll coefficient sequence. We prove that, for every integer $n\ge1$, the polynomial \[ M_n(x)=\sum_{i=0}^n \bigl(d_i(n)^2-d_{i-1}(n)d_{i+1}(n)\bigr)x^i \] has only simple negative zeros, which strictly interlace those of the Narayana polynomial of the same degree. This proves a conj...

Matthew H. Y. Xie, Philip B. Zhang · 1 citation