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PreprintCC BY 4.0arXiv

A common interleaver for two antichain polynomials on [k]× Pn,s

  • Jian Ding
  • Lingen Ding
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Abstract

The first author and Dong \cite{DD} proposed three conjectures on antichain generating polynomials. Jiang \cite{Jiang} recently proved Conjectures 4.3 and 4.5, concerning real-rootedness and γ-positivity. We prove Conjecture 4.2 by adapting his method from [k]× [2] × [n] to [k]× Pn,s, where Pn,s is a two-row Ferrers shape. We establish real stability for a family of bivariate polynomials associated with adjacent shapes, then apply the Chudnovsky-Seymour compatibility criterion to obtain a common interleaver. As noted in \cite{DD}, Conjecture 4.2 also implies Conjecture 4.3.

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Cite

BibTeXRIS
BibTeX
@misc{ding2026common,
  title = {{A common interleaver for two antichain polynomials on $[k]$$\times$ $P_n,s$}},
  author = {Jian Ding and Lingen Ding},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.25717},
  eprint = {2609.25717},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.25717},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A common interleaver for two antichain polynomials on [k]× P_n,s
AU  - Jian Ding
AU  - Lingen Ding
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2609.25717
UR  - https://arxiv.org/abs/2609.25717
AB  - The first author and Dong \cite{DD} proposed three conjectures on antichain generating polynomials. Jiang \cite{Jiang} recently proved Conjectures 4.3 and 4.5, concerning real-rootedness and γ-positivity. We prove Conjecture 4.2 by adapting his method from [k]× [2] × [n] to [k]× P_n,s, where P_n,s is a two-row Ferrers shape. We establish real stability for a family of bivariate polynomials associated with adjacent shapes, then apply the Chudnovsky-Seymour compatibility criterion to obtain a common interleaver. As noted in \cite{DD}, Conjecture 4.2 also implies Conjecture 4.3.
ER  -