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Minimal Balanced Neighborly Polynomials
Satoshi Murai
,
Nguyen Thi Thanh Tam
Abstract
In this paper we introduce minimal balanced neighborly polynomials and show some methods to construct such polynomials. In particular, using this notion, we prove the existence of balanced neighborly polynomials of the following types: (i) type $(p,\dots ,p)$ for most prime numbers $p$, (ii) types $(d-1,d,d,d)$, $(d-1,d-1,d,d)$ and $(d-1,d-1,d-1,d)$ when d is odd or is divisible by 4. We also construct balanced neighborly simplicial spheres of type $(2,4k-1,4k-1,4k-1)$.