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Journal of Algebraic Combinatorics

, Volume 48, Issue 2, pp 325–349 | Cite as

Warning’s second theorem with relaxed outputs

  • Pete L. Clark
Article

Abstract

We present a generalization of Warning’s second theorem to polynomial systems over a finite local principal ring with restricted input and relaxed output variables. This generalizes a recent result with Forrow and Schmitt (and gives a new proof of that result). Applications to additive group theory, graph theory and polynomial interpolation are pursued in detail.

Keywords

Polynomial method Polynomial congruences Restricted variables Davenport constant Divisible graph 

Notes

Acknowledgements

Thanks to Dino Lorenzini, Paul Pollack, Bob Rumely and Lori D. Watson for helpful discussions. Thanks to J.R. Schmitt for introducing me to this rich circle of ideas, for many helpful remarks, and for Example 3.2. I am grateful to the referee for an extraordinarily careful, detailed and informative report.

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Authors and Affiliations

  1. 1.University of GeorgiaAthensUnited States

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