In this paper, we consider multivariate hyperedge elimination polynomials and multivariate chromatic polynomials for hypergraphs. The first set of polynomials is defined in terms of a deletion-contraction-extraction recurrence, previously investigated for graphs by Averbouch, Godlin, and Makowsky. The multivariate chromatic polynomial is an equivalent polynomial defined in terms of colorings, and generalizes the coboundary polynomial of Crapo, and the bivariate chromatic polynomial of Dohmen, Pönitz and Tittman. We show that specializations of these new polynomials recover polynomials which enumerate hyperedge coverings, matchings, transversals, and section hypergraphs. We also prove that the polynomials can be defined in terms of Möbius inversion on the bond lattice of a hypergraph, as well as compute these polynomials for various classes of hypergraphs.
The balanced upper chromatic number of linear hypergraphs and the $n$-cube over $t$ elements
Universidad Nacional Autónoma de México（墨西哥国立自治大学）；California State University, Northridge（北岭加州州立大学）；Centro de Investigación y Estudios de Posgrado del IPN（墨西哥国立理工学院研究生研究与评价中心）
On the largest chromatic number of $F$-free hypergraphs
Tsinghua University（清华大学）；Northwestern Polytechnical University（西北工业大学）；Alfréd Rényi Institute of Mathematics（阿尔弗雷德·雷尼数学研究所）；Budapest University of Technology and Economics（布达佩斯技术与经济大学）
On colorings of hypergraphs embeddable in $\mathbb{R}^d$
Keimyung University（启明大学）；Einstein Institute of Mathematics, Hebrew University（希伯来大学爱因斯坦数学研究所）；Mathematics Research Institute, Universidad de Valladolid（瓦拉多利德大学数学研究所）；CMSA, Harvard University（哈佛大学数学与统计应用中心）
