| Autor: |
Gao, Jiyang, Marx-Kuo, Jared, McDonald, Vaughan, Yuen, Chi Ho |
| Předmět: |
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| Zdroj: |
Communications in Algebra; 2024, Vol. 52 Issue 10, p4459-4479, 21p |
| Abstrakt: |
The sandpile group of a connected graph G, defined to be the torsion part of the cokernel of the graph Laplacian, is a subtle graph invariant with combinatorial, algebraic, and geometric descriptions. Extending and improving previous works on the sandpile group of hypercubes, we study the sandpile groups of the Cayley graphs of F 2 r , focusing on their poorly understood Sylow-2 component. We find the number of Sylow-2 cyclic factors for "generic" Cayley graphs and deduce a bound for the non-generic ones. Moreover, we provide a sharp upper bound for their largest Sylow-2 cyclic factors. In the case of hypercubes, we give exact formulae for the largest n–1 Sylow-2 cyclic factors. Some key ingredients of our work include the natural ring structure on these sandpile groups from representation theory, and calculation of the 2-adic valuations of binomial sums via the combinatorics of carries. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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