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math.CO2024
Sensitivity of -ary functions and low degree partitions of Hamming graphs
Sara Asensio, Ignacio García-Marco, Kolja Knauer
The study of complexity measures of Boolean functions led Nisan and Szegedy to state the sensitivity conjecture in 1994, claiming a polynomial relation between degree and sensitivi…
math.CO2024
Coloring minimal Cayley graphs
Ignacio García-Marco, Kolja Knauer
In 1978 Babai raised the question whether all minimal Cayley graphs have bounded chromatic number; in 1994 he conjectured a negative answer. In this paper we show that any minimal…
math.AC2024
Proyective Cohen-Macaulay monomial curves and their affine charts
Ignacio García-Marco, Philippe Gimenez, Mario González-Sánchez
In this paper, we explore when the Betti numbers of the coordinate rings of a projective monomial curve and one of its affine charts are identical. Given an infinite field and…