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 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…
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,Ï}(x,y)=\sum_{\substack{p_{1}(n)> y\\ n\leq x} } μ(n) {Ï(n)-1…
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…
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…