2014/12/08 by Gleb Nenashev, Nenashev, Gleb
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Algebra over a field #Algebra representation #Cellular algebra #Combinatorics #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #Commutative property #Computer science #Construct (python library) #Dimension (graph theory) #Discrete mathematics #Division algebra #FOS: Mathematics #Filtered algebra #Graph #Graph Labeling and Dimension Problems #Graph algebra #Incidence algebra #Line graph #Mathematical analysis #Mathematics #Polynomial #Pure mathematics #Symmetric algebra #Tutte polynomial #Voltage graph #math.AC #math.CO
paper · pdf · doi:10.48550/arxiv.1412.2561
arxiv created 2014/12/08 · openalex publication_date 2014/12/08 · arxiv updated 2014/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a given graph G, we construct an associated commutative algebra, whose dimension is equal to the number of t-labeled forests of G. We show that the dimension of the k-th graded component of this algebra also has a combinatorial meaning and that its Hilbert polynomial can be expressed through the Tutte polynomial of G.