Year: 2020
Type: preprint
Abstract: We initiate the study of enumerating linear subspaces of alternating matrices over finite fields with explicit coordinates. We postulate that this study can be viewed as a linear algebraic analogue of the classical topic of enumerating labelled graphs. To support this viewpoint, we present q-analogues of Gilbert's formula for enumerating connected graphs (Can. J. Math., 1956), and Read's formula for enumerating c-colored graphs (Can. J. Math., 1960). We also develop an analogue of Riddell's formula relating the exponential generating function of graphs with that of connected graphs (Riddell's PhD thesis, 1951), building on Eulerian generating functions developed by Srinivasan (Discrete Math., 2006).
Source: arXiv (Cornell University)
Author: Qiao, Youming
Institution: University of Technology Sydney
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3040939452