Order Quasisymmetric Functions Distinguish Rooted Trees

Richard P. Stanley conjectured that finite trees can be distinguished by their chromatic symmetric functions. In this paper, we prove an analogous statement for posets: Finite rooted trees can be distinguished by their order quasisymmetric functions.Comment: 16 pages, 5 figures, referees' suggestions incorporate

Freeness of Hyperplane Arrangements between Boolean Arrangements and Weyl Arrangements of Type Bℓ B_{\ell}

Every subarrangement of Weyl arrangements of type $B_{\ell}$ is represented by a signed graph. Edelman and Reiner characterized freeness of subarrangements between type $A_{\ell-1}$ and type $B_{\ell}$ in terms of graphs. Recently, Suyama and the authors characterized freeness for subarrangements containing Boolean arrangements satisfying a certain condition. This article is a sequel to the previous work. Namely, we give a complete characterization for freeness of arrangements between Boolean arrangements and Weyl arrangements of type $B_{\ell}$ in terms of graphs.Comment: 15 page

A Generalization of APN Functions for Odd Characteristic

Almost perfect nonlinear (APN) functions on finite fields of characteristic two have been studied by many researchers. Such functions have useful properties and applications in cryptography, finite geometries and so on. However APN functions on finite fields of odd characteristic do not satisfy desired properties. In this paper, we modify the definition of APN function in the case of odd characteristic, and study its properties