English

Races among products

Combinatorics 2013-11-22 v3 Number Theory

Abstract

We will revisit a 1987 question of Rabbi Ehrenpreis. Among many things, we will provide an elementary injective proof that P_1(L,y,n)>=P_2(L,y,n) for any L,n>0 and any odd y>1 . Here, P_1(L,y,n) denotes the number of partitions of n into parts congruent to 1, y+2, or 2y mod 2(y+1) with the largest part not exceeding 2(y+1)L-2 and P_2(L,y,n) denotes the number of partitions of n into parts congruent to 2, y, or 2y+1 mod 2(y+1) with the largest part not exceeding 2(y+1)L-1.

Keywords

Cite

@article{arxiv.1112.3392,
  title  = {Races among products},
  author = {Alexander Berkovich and Keith Grizzell},
  journal= {arXiv preprint arXiv:1112.3392},
  year   = {2013}
}

Comments

9 pages, 1 table

R2 v1 2026-06-21T19:51:33.716Z