Room 326

Skeleton ideals of graphs

Gargi Lather

IIT Madras

Graphical parking functions are an interesting generalisation of classical parking functions, independently
developed and studied by various authors. This generalised notion was defined from an algebraic perspective by Postnikov and
Shapiro in their seminal work in 2004. For a graph G with a designated vertex as root, they associated a G-parking function
ideal in the standard polynomial ring over a field with variables corresponding to the non-root vertices of G. The standard
monomials of this ideal, given by the G-parking functions, are in bijective correspondence with the spanning trees of G.
Recently, Dochtermann introduced and investigated the k-skeleton ideals, which are certain parameter-dependent subideals of
the G-parking function ideal. In this talk, we will be discussing some combinatorial properties of these k-skeleton ideals.