#### 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.

Done