Races among products

Details Races among products Races among products

2011-12-14

arxiv.org/abs/1112.3392v2

Mathematics

Combinatorics

9 pages, 1 table

Scientific paper

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.

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