English

The balancing index over the alternating group

Combinatorics 2024-08-15 v1 Group Theory

Abstract

The balancing index of a polynomial fZ[x1,,xn]f \in \mathbb{Z}[x_1,\dots,x_n] is the least positive sum of coefficients in an integer linear combination of permuted copies of ff which produces a symmetric polynomial. Here we consider the restricted problem in which only even permutations are used.

Keywords

Cite

@article{arxiv.2408.07679,
  title  = {The balancing index over the alternating group},
  author = {Peter Dukes and Georgia Penner},
  journal= {arXiv preprint arXiv:2408.07679},
  year   = {2024}
}
R2 v1 2026-06-28T18:13:03.637Z