Generating functions are constructed for black-white polynomials of graphs, yielding rational forms for certain families, a matrix model for the exponential generating function over all graphs, and extensions for graphs with fixed loop number.
Gunnells, Tim Coopmans, and Jordi Tura, Sec- tor length distributions of recursively definable graph sta tes through analytic combinatorics , preprint, 2026
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Black-white polynomials of graphs and generating functions
Generating functions are constructed for black-white polynomials of graphs, yielding rational forms for certain families, a matrix model for the exponential generating function over all graphs, and extensions for graphs with fixed loop number.