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papers

Publications (5)

math.CO2026

On the computations of the Cullis' determinant

Alexander Guterman, Andrey Yurkov

The Cullis' determinant is a generalization of the ordinary determinant for rectangular matrices. It is defined as the alternating sum of maximal minors of a given matrix. In this…

math.CO2026

Linear varieties and matroids with applications to the Cullis' determinant

Alexander Guterman, Andrey Yurkov

Let $V$ be a vector space of rectangular $n \times k$ matrices annihilating the Cullis' determinant. We show that $dim (V) \leq (n - 1) k$ , extending Dieudonn{Ã©}'s result on the dimens…

math.CO2026

Nonlinear maps preserving the polynomial

Andrey Yurkov

Let $F$ be a field and $P \in F [x_{1}, \dots, x_{n}]$ be a homogeneous polynomial such that $∣ F ∣ > A^° (P)$ and $I ¨ , I ¨ : F^{n} \to F^{n}$ be two…

math.CO2026

Linear maps preserving the Cullis' determinant. II

Alexander Guterman, Andrey Yurkov

This paper is the second in the series of papers devoted to the explicit description of linear maps preserving the Cullis' determinant of rectangular matrices with entries belongin…

math.CO2025

Linear maps preserving the Cullis' determinant. I

Alexander Guterman, Andrey Yurkov

This paper is the first in the series of papers devoted to the explicit description of linear maps preserving the Cullis' determinant of rectangular matrices with entries belonging…