3 fixed some typos

Possible articles you might have seen could be

M.V. Subbarao, Partition theorems for Euler pairs, Proc. Amer. Math. Soc. 28 (1971), no. 2, 330-336.

Hre

Here the author characterizes all triples $(A,B,r)$ so that the number of partitions with parts in $A$ is equal to the number of partitions with parts in $B$ with no part repeated more than $r-1$ times. These are the sets satisfying $rB\subset B$ and $A=B-rB$.

J.B. Remmel, Bijective Proofs of Some Classical Partition Identities, J. Combin. Theory Ser. A 33 (1982), 273–286

This paper proves a very general statement phrased in terms of forbidden patterns. Namely given two sequences of non-empty multisets $\mathcal A=\lbrace A_i\rbrace _{i\in \omega}$ and $\mathcal B=\lbrace B_i\rbrace _{i\in \omega}$, let $|M|$ denote the sum of the elements in $M$ as a multiset. Then if $$|\bigcup _{i\in S} A_i|=|\bigcup _{i\in S} B_i|$$ holds for all $S\subset \omega$, the number of partitions with no $\mathcal A$ patterns is equal to the number of partitions with no $\mathcal B$ patterns.

K.M. O’Hara, Bijections for Partition Identities, J. Combin. Theory Ser. A 49 (1988), 13–25.

While Remmel's approach gives a bijection basd based on the Garsia-Milne involution, this paper shows that the algorithm for producing bijections can be made considerably faster at least in the case of disjoint multisets.

On the other hand, it could have been a more recent article which most probably references at least one of these papers. You can find an extended list of references as well as various statements which generalize the bijection you mention, in Igor Pak's survey on partition bijections, the relevant section being section 8 (survey is also available from his website). This is also the topic of Herbert S. Wilf's notes "Lectures on Integer Partitions" (which you an can find here).

2 added 1170 characters in body

Hre the author characterizes all triples $(A,B,r)$ so that the number of partitions with parts in $A$ is equal to the number of partitions with parts in $B$ with no part repeated more than $r-1$ times. These are the sets satisfying $rB\subset B$ and $A=B-rB$.

This paper proves a very general statement phrased in terms of forbidden patterns. Namely given two sequences of non-empty multisets $\mathcal A=\lbrace A_i\rbrace _{i\in \omega}$ and $\mathcal B=\lbrace B_i\rbrace _{i\in \omega}$, let $|M|$ denote the sum of the elements in $M$ as a multiset. Then if $$|\bigcup _{i\in S} A_i|=|\bigcup _{i\in S} B_i|$$holds for all $S\subset \omega$, the number of partitions with no $\mathcal A$ patterns is equal to the number of partitions with no $\mathcal B$ patterns.

Or

While Remmel's approach gives a bijection basd on the Garsia-Milne involution, this paper shows that the algorithm for producing bijections can be made considerably faster at least in the case of disjoint multisets.

On the other hand, it could have been a more recent article which most probably references at least one of these papers. You can find an extended list of references as well as various statements which generalize the bijection you mention, in Igor Pak's survey on partition bijections, the relevant section being section 8 (survey is also available from his website). This is also the topic of Herbert S. Wilf's notes "Lectures on Integer Partitions" (which you an find here).

1

Possible articles you might have seen could be

M.V. Subbarao, Partition theorems for Euler pairs, Proc. Amer. Math. Soc. 28 (1971), no. 2, 330-336.

J.B. Remmel, Bijective Proofs of Some Classical Partition Identities, J. Combin. Theory Ser. A 33 (1982), 273–286

K.M. O’Hara, Bijections for Partition Identities, J. Combin. Theory Ser. A 49 (1988), 13–25.

Or it could have been a more recent article which most probably references at least one of these papers. You can find an extended list of references as well as various statements which generalize the bijection you mention, in Igor Pak's survey on partition bijections, the relevant section being section 8 (survey is also available from his website).