Torsten Ueckerdt introduced t he invariant called local dimension which, instead, uses partial linear ext ensions and which is bounded above by the Dushnik-Miller dimension. For ins tance, the dimension of the standard example of order $n$ is $n/2$, but the local dimension is only $3$.

In this talk, we study the local dim ension of show that the maximum local dimension of a poset of order n is $\ Theta(n/\log n)$, the local dimension of the $n$-dimensional Boolean lattic e is at least $\Theta(n/\log n)$ and make progress toward resolving a versi on of the removable pair conjecture for local dimension. We also connect th e computation of local dimension of a poset to the decomposition of the edg es of a graph into what are called difference graphs.

This is join t work with Jinha Kim (Seoul National University), Tomás Masarík (Charles U niversity), Warren Shull (Emory University), Heather C. Smith (Davidson Col lege), Andrew Uzzell (Holy Cross College), and Zhiyu Wang (University of So uth Carolina) as a part of the 2017 Graduate Research Workshop in Combinato rics. DTSTAMP:20210926T175655Z DTSTART;TZID=Europe/Budapest:20191115T100000 DTEND;TZID=Europe/Budapest:20191115T120000 SEQUENCE:0 TRANSP:OPAQUE END:VEVENT END:VCALENDAR