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math.AC2020
A truncated minimal free resolution of the residue field
Van C. Nguyen, Oana Veliche
In a paper in 1962, Golod proved that the Betti sequence of the residue field of a local ring attains an upper bound given by Serre if and only if the homology algebra of the Koszu…
math.CO2020
Minors of a skew symmetric matrix: A combinatorial approach
Lars Winther Christensen, Oana Veliche, Jerzy Weyman
We use Knuth's combinatorial approach to Pfaffians to reprove and clarify a century-old formula, due to Brill. It expresses arbitrary minors of a skew symmetric matrix in terms of…