BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Lu Liu (Central South University) DTSTART:20200617T010000Z DTEND:20200617T020000Z DTSTAMP:20260404T131149Z UID:CTA/9 DESCRIPTION:Title: The coding power of products of partitions\nby Lu Liu (Central Sout h University) as part of Computability theory and applications\n\n\nAbstra ct\nGiven two combinatorial notions P0 and P1\, can we encode P0 via P1. In this talk we address the question where P0 is a 3-partition of integers and P1 is a product of finitely many 2-partitions of integers.\n We firstly reduce the question to a lemma which asserts that certain Pi01 cla ss of partitions admit two members violating a particular combinatorial co nstraint. Then we took a digression to see how complex does the class has to be so as to maintain the cross constraint. \n On the other hand\, reducing the complexity of the two members in the lemma in certain ways w ill answer an open question concerning a sort of Weihrauch degree of stabl e Ramsey's theorem for pairs. It turns out the resulted strengthen of the lemma is a basis theorem for Pi01 class with additional constraint. We loo k at several such variants of basis theorem\, among them some are unknown. \n We end up by introducing some results and questions concerning p roduct of infinitely many partitions.\n LOCATION:https://stable.researchseminars.org/talk/CTA/9/ END:VEVENT END:VCALENDAR