BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Carles Padró (Universitat Politècnica de Catalunya) DTSTART:20260311T160000Z DTEND:20260311T171500Z DTSTAMP:20260423T021324Z UID:AAIT/50 DESCRIPTION:Title: In teraction between skew-representability\, tensor products\, extension prop erties\, and rank inequalities.\nby Carles Padró (Universitat Politè cnica de Catalunya) as part of Seminar on Algorithmic Aspects of Informati on Theory\n\n\nAbstract\nSkew-representable matroids form a fundamental cl ass in matroid theory\, bridging combinatorics and linear algebra. They pl ay an important role in areas such as coding theory\, optimization\, and c ombinatorial geometry\, where linear structure is crucial for both theoret ical insights and algorithmic applications. Since deciding skew-representa bility is computationally intractable\, much effort has been focused on id entifying necessary or sufficient conditions for a matroid to be skew-repr esentable.\n\nIn this paper\, we introduce a novel approach to studying sk ew-representability and structural properties of matroids and polymatroid functions via tensor products. We provide a characterization of skew-repre sentable matroids\, as well as of those representable over skew fields of a given prime characteristic\, in terms of tensor products. As an algorith mic consequence\, we show that deciding skew-representability\, or represe ntability over a skew field of fixed prime characteristic\, is co-recursiv ely enumerable: that is\, certificates of non-skew-representability — in general or over a fixed prime characteristic — can be verified. We also prove that every rank-3 matroid admits a tensor product with any uniform matroid and give a construction yielding the unique freest tensor product in this setting. Finally\, as an application of the tensor product framewo rk\, we give a new proof of Ingleton's inequality and\, more importantly\, derive the first known linear rank inequality for folded skew-representab le matroids that does not follow from the common information property.\n LOCATION:https://researchseminars.org/talk/AAIT/50/ END:VEVENT END:VCALENDAR