Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Invertible minor assignment and complexity of set-valued functions   We introduce an algebraic model based on the expansion of the determinant of
two matrices to provide a criterion for the additivity of Z^d-valued set
functions. Each individual term of the expansion is deformed through a monomial
factor in d indeterminates with exponents defined by the set function. A family
of sparse polynomials is derived from the coupling of Grassmann-Plucker
relations for the two matrices, and its factorisation properties in the ring of
Laurent polynomials are studied.
  In this work, we focus on matrices satisfying a given generic condition to
prove that such a deformation returns a determinantal expansion if and only if
it is induced by a diagonal matrix of units in the ring of Laurent polynomials
acting as a kernel into the initial determinant expansion, which guarantees the
additivity of the set function. This result is applied to explore complexity
reduction for set functions, with special attention to permutations of families
of subsets.

13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom