All reports by Author Prasad Chaugule:

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TR24-021
| 29th January 2024
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Prasad Chaugule, Nutan Limaye#### On the closures of monotone algebraic classes and variants of the determinant

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TR20-152
| 7th October 2020
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Prasad Chaugule, Nutan Limaye, Shourya Pandey#### Variants of the Determinant polynomial and VP-completeness

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TR19-172
| 28th November 2019
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Prasad Chaugule, Mrinal Kumar, Nutan Limaye, Chandra Kanta Mohapatra, Adrian She, Srikanth Srinivasan#### Schur Polynomials do not have small formulas if the Determinant doesn't!

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TR18-135
| 31st July 2018
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Prasad Chaugule, Nutan Limaye, Aditya Varre#### Variants of Homomorphism Polynomials Complete for Algebraic Complexity Classes

Revisions: 1

Prasad Chaugule, Nutan Limaye

In this paper we prove the following two results.

* We show that for any $C \in {mVF, mVP, mVNP}$, $C = \overline{C}$. Here, $mVF, mVP$, and $mVNP$ are monotone variants of $VF, VP$, and $VNP$, respectively. For an algebraic complexity class $C$, $\overline{C}$ denotes the closure of $C$. ...
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Prasad Chaugule, Nutan Limaye, Shourya Pandey

The determinant is a canonical VBP-complete polynomial in the algebraic complexity setting. In this work, we introduce two variants of the determinant polynomial which we call $StackDet_n(X)$ and $CountDet_n(X)$ and show that they are VP and VNP complete respectively under $p$-projections. The definitions of the polynomials are inspired by a ... more >>>

Prasad Chaugule, Mrinal Kumar, Nutan Limaye, Chandra Kanta Mohapatra, Adrian She, Srikanth Srinivasan

Schur Polynomials are families of symmetric polynomials that have been

classically studied in Combinatorics and Algebra alike. They play a central

role in the study of Symmetric functions, in Representation theory [Sta99], in

Schubert calculus [LM10] as well as in Enumerative combinatorics [Gas96, Sta84,

Sta99]. In recent years, they have ...
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Prasad Chaugule, Nutan Limaye, Aditya Varre

We present polynomial families complete for the well-studied algebraic complexity classes VF, VBP, VP, and VNP. The polynomial families are based on the homomorphism polynomials studied in the recent works of Durand et al. (2014) and Mahajan et al. (2016). We consider three different variants of graph homomorphisms, namely injective ... more >>>