From Independent Sets and Vertex Colorings to Isotropic Spaces and Isotropic Decompositions: Another Bridge Between Graphs and Alternating Matrix Spaces

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).

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From Independent Sets and Vertex Colorings to Isotropic Spaces and Isotropic Decompositions: Another Bridge Between Graphs and Alternating Matrix Spaces

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On the Baer-Lovász-Tutte construction of groups from graphs: isomorphism types and homomorphism notions

On the Baer-Lovász-Tutte construction of groups from graphs: isomorphism types and homomorphism notions

Enumerating alternating matrix spaces over finite fields with explicit coordinates

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