Algebraic Combinatorics on Trace Monoids: Extending Number Theory to Walks on Graphs

DOI10.1137/15M1054535zbMath1366.05049arXiv1601.01780MaRDI QIDQ5275437

Pierre-Louis Giscard, Paul Rochet

Publication date: 14 July 2017

Published in: SIAM Journal on Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1601.01780

zbMATH Keywords

posetdigraphwalksIhara zeta functionincidence algebraweighted adjacency matrixtrace monoidMacMahon master theorem

Mathematics Subject Classification ID

Paths and cycles (05C38) Algebraic combinatorics (05E99) Algebraic aspects of posets (06A11) Signed and weighted graphs (05C22)

Related Items (5)

BPS operators in \( \mathcal{N}=4 \) SO(\(N\)) super Yang-Mills theory: plethysms, dominoes and words ⋮ Counting walks by their last erased self-avoiding polygons using sieves ⋮ Realizable cycle structures in digraphs ⋮ A Hopf algebra for counting cycles ⋮ A coupling of the spectral measures at a vertex

Cites Work

• Almost all trees are co-immanantal
• Determinants and Möbius functions in trace monoids
• Computing the average parallelism in trace monoids.
• Quivers, words and fundamentals
• Combinatorial problems of commutation and rearrangements
• Evaluating Matrix Functions by Resummations on Graphs: The Method of Path-Sums
• Self-Avoiding Paths and the Adjacency Matrix of a Graph
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