Add to ORKGWe denote by spt(n) the total number of appearances of the small-est part in each integer partition of n. We shall relate spt(n) to the Atkin–Garvan moments of ranks, and we shall prove that 5|spt(5n+4), 7|spt(7n+ 5) and 13|spt(13n+ 6).
Atkin and Garvan introduced the moments of ranks of partitions in their work connecting ranks and cr...
AbstractWe prove a central limit theorem for the number of different part sizes in a random integer ...
AbstractSzekeres proved, using complex analysis, an asymptotic formula for the number of partitions ...
Let spt(n) denote the total number of appearances of the smallest parts in all the partitions of n. ...
Let spt(n) denote the total number of appearances of the smallest parts in all the partitions of n. ...
Let spt(n) denote the total number of appearances of the smallest parts in all the partitions of n. ...
We obtain a combinatorial proof of a surprising weighted partition equality of Berkovich and Uncu. O...
George E Andrews derived formula for the number of smallest parts of partitions of a positive intege...
Let spt (n) denote the total number of appearances of the smallest part in each partition of n. In 1...
In 2013, Andrews, Garvan and Liang defined Self-conjugate S-partitions. In 2011, Andrews stated the ...
In this article the rank of a partition of an integer is a certain integer associated with the parti...
We present two analogues of two well-known elementary arguments for a lower bound for p(n), the numb...
Andrews, Garvan and Liang introduced the spt-crank for vector partitions. We conjecture that for any...
We present two analogues of two well-known elementary arguments for a lower bound for p(n), the numb...
In 1916, Ramanujan’s showed the spt-crank for marked overpartitions. The corresponding special funct...
Atkin and Garvan introduced the moments of ranks of partitions in their work connecting ranks and cr...
AbstractWe prove a central limit theorem for the number of different part sizes in a random integer ...
AbstractSzekeres proved, using complex analysis, an asymptotic formula for the number of partitions ...
Let spt(n) denote the total number of appearances of the smallest parts in all the partitions of n. ...
Let spt(n) denote the total number of appearances of the smallest parts in all the partitions of n. ...
Let spt(n) denote the total number of appearances of the smallest parts in all the partitions of n. ...
We obtain a combinatorial proof of a surprising weighted partition equality of Berkovich and Uncu. O...
George E Andrews derived formula for the number of smallest parts of partitions of a positive intege...
Let spt (n) denote the total number of appearances of the smallest part in each partition of n. In 1...
In 2013, Andrews, Garvan and Liang defined Self-conjugate S-partitions. In 2011, Andrews stated the ...
In this article the rank of a partition of an integer is a certain integer associated with the parti...
We present two analogues of two well-known elementary arguments for a lower bound for p(n), the numb...
Andrews, Garvan and Liang introduced the spt-crank for vector partitions. We conjecture that for any...
We present two analogues of two well-known elementary arguments for a lower bound for p(n), the numb...
In 1916, Ramanujan’s showed the spt-crank for marked overpartitions. The corresponding special funct...
Atkin and Garvan introduced the moments of ranks of partitions in their work connecting ranks and cr...
AbstractWe prove a central limit theorem for the number of different part sizes in a random integer ...
AbstractSzekeres proved, using complex analysis, an asymptotic formula for the number of partitions ...