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2 results

  • A result on the $c_2$ invariant for powers of primes

  • Part of
  • Maria S. Esipova, Karen Yeats
  • Journal:
    Canadian Mathematical Bulletin / Volume 66 / Issue 4 / December 2023
    Published online by Cambridge University Press:
    24 April 2023, pp. 1164-1178
    Print publication:
    December 2023
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  • The $c_2$ invariant is an arithmetic graph invariant related to quantum field theory. We give a relation modulo p between the $c_2$ invariant at p and the $c_2$ invariant at $p^s$ by proving a relation modulo p between certain coefficients of powers of products of particularly nice polynomials. The relation at the level of the $c_2$ invariant provides evidence for a conjecture of Schnetz.

  • SOME RESULTS ON AN ALGEBRO-GEOMETRIC CONDITION ON GRAPHS

  • Part of
  • AVI KULKARNI, GREGORY MAXEDON, KAREN YEATS
  • Journal:
    Journal of the Australian Mathematical Society / Volume 104 / Issue 2 / April 2018
    Published online by Cambridge University Press:
    29 March 2017, pp. 218-254
    Print publication:
    April 2018
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  • Paolo Aluffi, inspired by an algebro-geometric problem, asked when the Kirchhoff polynomial of a graph is in the Jacobian ideal of the Kirchhoff polynomial of the same graph with one edge deleted. We give some results on which graph–edge pairs have this property. In particular, we show that multiple edges can be reduced to double edges, we characterize which edges of wheel graphs satisfy the property, we consider a stronger condition which guarantees the property for any parallel join, and we find a class of series–parallel graphs with the property.