On the Algebraic Combinatorics of Injections and its Applications to Injection Codes

Peter J. Dukes; Ferdinand Ihringer; Nathan Lindzey

On the Algebraic Combinatorics of Injections and its Applications to Injection Codes

Combinatorics 2019-12-11 v1

Authors: Peter J. Dukes , Ferdinand Ihringer , Nathan Lindzey

Abstract

We consider the algebraic combinatorics of the set of injections from a $k$ -element set to an $n$ -element set. In particular, we give a new combinatorial formula for the spherical functions of the Gelfand pair $(S_k \times S_n, \text{diag}(S_k) \times S_{n-k})$ . We use this combinatorial formula to give new Delsarte linear programming bounds on the size of codes over injections.

Keywords

algebraic combinatorics injections gelfand pair spherical functions injection codes delsarte bounds

Cite

@article{arxiv.1912.04500,
  title  = {On the Algebraic Combinatorics of Injections and its Applications to Injection Codes},
  author = {Peter J. Dukes and Ferdinand Ihringer and Nathan Lindzey},
  journal= {arXiv preprint arXiv:1912.04500},
  year   = {2019}
}

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18 pages

On the Algebraic Combinatorics of Injections and its Applications to Injection Codes

Abstract

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