About

Professor Krishnaswami Alladi is associated with the Department of Mathematics at the University of Florida, located in Gainesville, FL. His academic autobiography titled "My Mathematical Universe – People, Personalities and the Profession" was published by World Scientific Publishing Company in 2022. The book reflects his personal journey and experiences within the mathematical community. He is actively involved in the mathematical profession, contributing to the academic and professional development of the field. His contact information includes a phone number, fax, and email address, indicating his openness to academic correspondence and collaboration. The webpage also mentions his presence at notable events such as the American Mathematical Society Annual Meeting, highlighting his engagement with the broader mathematical community.

Research topics

• Computer Science
• History
• Sociology
• Pure mathematics
• Mathematics
• Psychotherapist
• Psychology
• Geology
• Classics
• Philosophy
• Geography
• Environmental ethics
• Engineering
• Paleontology
• Art
• Aesthetics
• Ancient history
• Mechanical engineering
• Art history
• Theology

Selected publications

• Basis partitions and their signature

  ArXiv.org · 2025-07-19

  preprintOpen access1st authorCorresponding

  Basis partitions are minimal partitions corresponding to successive rank vectors. We show combinatorially how basis partitions can be generated from primary partitions which are equivalent to the Rogers-Ramanujan partitions. This leads to the definition of a signature of a basis partition that we use to explain certain parity results. We then study a special class of basis partitions which we term as complete. Finally we discuss basis partitions and minimal basis partitions among partitions with non-repeating odd parts by representing them using 2-modular graphs.

  PublisherOA PDFDOI

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

  Arabian Journal of Mathematics · 2025-11-15

  articleSenior author
  PublisherDOI

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

  ArXiv.org · 2025-02-07

  preprintOpen accessSenior author

  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 infinity, we get the 1993 Alladi-Gordon $q$-hypergeometric key-identity for the generalized Schur Theorem as well as the fundamental Lebesgue identity by two different choices of the variables. This polynomial identity provides a generalization and a unified approach to the Schur and Lebesgue theorems. We discuss other analytic identities for the Lebesgue and Schur theorems and also provide a key identity ($q$-hypergeometric) for Andrews' deep refinement of the Alladi-Schur theorem. Finally, we discuss a new infinite hierarchy of identities, the first three of which relate to the partition theorems of Euler, Lebesgue, and Capparelli, and provide their polynomial versions as well.

  PublisherOA PDFDOI

• Basis Partitions and Their Signature

  Symmetry Integrability and Geometry Methods and Applications · 2025-12-11

  articleOpen access1st authorCorresponding

  Basis partitions are minimal partitions corresponding to successive rank vectors. We show combinatorially how basis partitions can be generated from primary partitions which are equivalent to the Rogers-Ramanujan partitions. This leads to the definition of a signature of a basis partition that we use to explain certain parity results. We then study a special class of basis partitions which we term as complete. Finally, we discuss basis partitions and minimal basis partitions among partitions with non-repeating odd parts by representing them using 2-modular graphs.

  PublisherOA PDFDOI

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

  arXiv (Cornell University) · 2024-12-04

  preprintOpen access1st authorCorresponding

  Let $ν_y(n)$ denote the number of distinct prime factors of $n$ that are $

  PublisherOA PDFDOI

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

  arXiv (Cornell University) · 2024-10-23

  preprintOpen access1st authorCorresponding

  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 the following result as a consequence of the Prime Number Theorem for Arithmetic Progressions: If $k$ and $\ell$ are positive integers, with $1\le\ell\le k$ and $(\ell, k)=1$, then $$ \sum_{n\ge 2,\, p(n)\equiv\ell(mod\,k)}\frac{μ(n)}{n}=\frac{-1}{ϕ(k)}, $$ where $μ(n)$ is the Moebius function, $p(n)$ is the smallest prime factor of $n$, and $ϕ(k)$ is the Euler function. Here we utilize the next level Duality identity between the second largest prime factor and the smallest prime factor, involving the Moebius function and $ω(n)$, the number of distinct prime factors of $n$, to establish the following result as a consequence of the Prime Number Theorem for Arithmetic Progressions: For all $\ell$ and $k$ as above, $$ \sum_{n\ge 2, \, p(n)\equiv\ell(mod\,k)}\frac{μ(n)ω(n)}{n}=0. $$ A quantitative version of this result is proved.

  PublisherOA PDFDOI

• Preface

  The Ramanujan Journal · 2023-04-24

  articleOpen access1st authorCorresponding
  PublisherOA PDFDOI

• Schmidt-type theorems via weighted partition identities

  The Ramanujan Journal · 2022-09-14 · 3 citations

  article1st authorCorresponding
  PublisherDOI

• My Mathematical Universe

  WORLD SCIENTIFIC eBooks · 2022-05-31

  book1st authorCorresponding
  PublisherDOI

• Review of the Movie on the Mathematical Genius Ramanujan

  2021-01-01

  book-chapter1st authorCorresponding
  PublisherDOI

Frequent coauthors

• P. Erdős

  55 shared

• Alexander Bérkovich

  University of Florida

  22 shared

• George E. Andrews

  17 shared

• Steven G. Krantz

  Washington University in St. Louis

  7 shared

• Basil Gordon

  University of Oklahoma

  7 shared

• Ae Ja Yee

  Pennsylvania State University

  5 shared

• Frank G. Garvan

  5 shared

• Bruce C. Berndt

  5 shared

Education

• Ph.D., Mathematics

  University of Florida

  1978

• M.S., Mathematics

  University of Florida

  1975

• B.S., Mathematics

  University of Madras

  1973

Awards & honors

• Award of Honorary Doctorate by SASTRA University (2022)
• Ramanujan's Place in the World of Mathematics (2021)
• George E. Andrews 80 Years of Combinatory Analysis (2021)
• Ramanujan 125th Anniversary Book