Races among products
Abstract
We will revisit a 1987 question of Rabbi Ehrenpreis. Among many things, we will provide an elementary injective proof that P1(L,y,n)>=P2(L,y,n) for any L,n>0 and any odd y>1 . Here, P1(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 P2(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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