5 papers
Capparelli's partition theorem as part of an infinite hierarchy: Combinatorial and Weighted Words extensions of recent work
Yazan Alamoudi, Krishnaswami Alladi
In a recent paper, the authors introduced an infinite hierarchy of -hypergeometric identities, of which the first three orders, , , and , relate to the partition theore…
On subradically sifted sums related to Alladi's higher order duality between prime factors
Yazan Alamoudi
In this paper, I utilize a variant of the Selberg--Delange method to find quantitative estimates of the sums \[M_{k,ω}(x,y)=\sum_{\substack{p_{1}(n)> y\\ n\leq x} } μ(n) {ω(n)-1\ch…
On a nonnegativity conjecture of Andrews
Yazan Alamoudi
I settle a conjecture of Andrews related to the Alladi-Schur polynomials. In addition, I give further relations and implications to two families of polynomials related to the Allad…
Some -hypergeometric identities associated with partition theorems of Lebesgue, Schur and Capparelli
Yazan Alamoudi, Krishnaswami Alladi
Here, we establish a polynomial identity in three variables , and with the degree of the polynomial given in terms of two integers . By letting and tend to i…
A bijective proof of Andrews' refinement of the Alladi-Schur theorem
Yazan Alamoudi
This paper gives a bijective proof of Andrews' refinement of the Alladi-Schur theorem. Moreover, it demonstrates that the bijective framework introduced here can be used to reprodu…