Euler Medals recognize distinguished lifetime career contributions to combinatorial research by Fellows of the ICA who are still active in research. Normally, at most one medal per year is awarded.
Hall Medals recognize extensive quality research with substantial international impact by Fellows of the ICA in mid-career. Recipients must not have reached age 41 before the end of the year for which they are nominated. At most two medals per year are awarded.
Kirkman Medals recognize excellent research by Fellows or Associate Fellows of the ICA early in their research career, as evidenced by an excellent body of published research. Recipients must have earned their doctoral degree within the four years preceding the end of the year for which they are nominated. At most two medals per year are awarded.
Stanton Medals, instituted in 2016, honour significant lifetime contributions to promoting the discipline of combinatorics through advocacy, outreach, service, teaching and/or mentoring. Letters of nomination should establish the significance, duration, and impact of the nominees contributions other than research. At most one medal per year is to be awarded, typically to a Fellow of the ICA.
Each nomination for a medal is to be made by two or more Fellows of the ICA. No ICA medal can be awarded to a current member of the ICA Council; and no Kirkman, Hall, or Euler Medal can be awarded to an Honorary Fellow. Further, nominees for an Euler, Hall, or Kirkman medal must be ICA members in the year for which they are nominated. A nomination must include a complete curriculum vitae and a letter detailing the extent and importance of the nominee's contributions, addressing the selection criteria. Nomination letters should be suitable for inclusion, in whole or in part, in a citation that may appear in the Bulletin of the ICA.