K. Alladi

activity

20242026

collaborators

6 papers

math.NT2026

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 $q$ -hypergeometric identities, of which the first three orders, $0$ , $1$ , and $2$ , relate to the partition theore…

math.NT2026

Duality Between Prime Factors and The Prime Number Theorem For Arithmetic Progressions -- Higher Order Dualities

Krishnaswami Alladi, Sroyon Sengupta

In 1977, the first author observed a duality between the largest and smallest prime factors of integers, and established as a consequence some new results on the MÃ¶bius function $…

math.CO2025

Basis partitions and their signature

Krishnaswami Alladi

Basis partitions are minimal partitions corresponding to successive rank vectors. We show combinatorially how basis partitions can be generated from primary partitions which are eq…

math.NT2025

Some $q$ -hypergeometric identities associated with partition theorems of Lebesgue, Schur and Capparelli

Yazan Alamoudi, Krishnaswami Alladi

Here, we establish a polynomial identity in three variables $a, b, c$ , and with the degree of the polynomial given in terms of two integers $L, M$ . By letting $L$ and $M$ tend to i…

math.NT2024

Parity results concerning the generalized divisor function involving small prime factors of integers

Krishnaswami Alladi, Ankush Goswami

Let $I^½_{y} (n)$ denote the number of distinct prime factors of $n$ that are $< y$ . For $k$ a positive integer, and for $k + 2 \leq y \leq x$ , let $S_{- k} (x, y)$ denote the sum \begin{eqnar…

math.NT2024

Duality between prime factors and the Prime Number Theorem for Arithmetic Progressions -- II

Krishnaswami Alladi, Jason Johnson

In the first paper under this title (1977), the first author utilized a duality identity between the largest and smallest prime factors involving the Moebius function, to establish…