Books and Edited Volumes
(in reverse chronological order)
-
(with B. V. Limaye) A Course in Calculus and Real Analysis, Second Edition,
Undergraduate Texts in Mathematics,
Springer, New York, 2018, ix+538 pp.
[Click on the title to view the authors' Website of this book containing useful information and updates;
Click here to view the publisher's page of the book.]
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(coedited with A. Sathaye), Special issue of the
Journal of Algebra and Its Applications in honor of Shreeram S. Abhyankar, Vol. 14, No. 9 (2015); 14 Articles, 281 pp.
Contents
Foreword (PDF)
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(with B. V. Limaye) A Course in Multivariable Calculus and Analysis ,
Undergraduate Texts in Mathematics,
Springer, New York, 2010, xii+475 pp. (Corrected publication, 2019, xii+ 483 pp.)
[Click on the title to view the authors' Website of this book containing useful information and updates;
Click here to view the publisher's page of the book.]
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(coedited with A. R. Shastri, M. K. Srinivasan and
J. K. Verma),
Combinatorial Topology and Algebra, RMS Lecture Notes Series Vol. 18, Ramanujan Mathematical Society, Mysore, 2013, xiv+208 pp.
Frontmatter
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(with B. V. Limaye) A Course in Calculus and Real Analysis ,
Undergraduate Texts in Mathematics,
Springer, New York, 2006, x+432 pp..
[Click on the title to view the authors' Website of this book containing useful information and updates;
Click here to view the publisher's page of the book.]
[The Second Edition` is available since November 17, 2018, and is listed above).]
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(coedited with Hema Srinivasan and
J. K. Verma),
Commutative Algebra and Algebraic Geometry,
Contemporary Mathematics Vol. 390,
American Mathematical Society, Providence, 2005, xiv+173 pp.
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Papers
(in reverse chronological order)
[Many of these papers, and sometimes new ones not listed here, are also available on the arXiv.]
- (with Rati Ludhani)
On the minimum distance, minimum weight codewords, and the dimension of projective Reed-Muller codes, Advances in Mathematics of Communications, DOI: 10.3934/amc.2023035 (2023).
Abstract & Contents
PDF
- (with Rati Ludhani)
On the purity of resolutions of Stanley-Reisner rings associated to Reed-Muller codes, in: Algebra and Related Topics with Applications (Aligarh, India, December 2019),
M. Ashraf,
A. Ali and V. De Filippis Eds.,
Springer Proceedings in Mathematics & Statistics. Vol. 392, Springer, Singapore, 2022, pp. 325-335.
Abstract & Contents
MathSciNet
Zentralblatt
PDF
- (with Peter Beelen
and Mrinmoy Datta) A combinatorial approach to the number of solutions of systems of homogeneous polynomial equations over finite fields,
Moscow Mathematical Journal, Vol. 22, No. 4 (2022), pp. 565-593.
Abstract & Contents
MathSciNet
Zentralblatt
PDF
- (with Rakhi Pratihar and Tovohery H. Randrianarisoa) Shellability and homology of q-complexes and q-matroids,
Journal of Algebraic Combinatorics, Vol. 56, No. 4 (2022), pp. 1135-1162.
Abstract & Contents
MathSciNet
Zentralblatt
PDF
- (with Christophe Ritzenthaler, François Rodier,
and Michael A. Tsfasman)
Arithmetic, Geometry, and Coding Theory: Homage to
Gilles Lachaud,
in: Arithmetic, Geometry, Cryptography and Coding Theory (Luminy, France, May 2019),
S. Ballet, G. Bisson, and I. Bouw Eds.,
Contemporary Mathematics, Vol. 770, American Mathematical Society, Providence, RI, 2021, pp. 131-150.
Abstract & Contents
MathSciNet
Zentralblatt
PDF
- (with Trygve Johnsen) A polymatroid approach to generalized weights of rank metric codes,
Designs, Codes and Cryptography, Vol. 88, No. 12
(2020), pp. 2531-2546. (Available Online)
Abstract & Contents
Review from MathSciNet
Review from Zentralblatt
PDF
- (with Prasant Singh)
Pure resolutions, linear codes, and Betti numbers,
Journal of Pure and Applied Algebra,
Vol. 224, No. 10 (2020), Art. 106385, 22 pp.
Abstract & Contents
Review from MathSciNet
Review from Zentralblatt
PDF
- (with Peter Beelen)
Hyperplane sections of determinantal varieties over finite
fields and linear codes,
Discrete
Mathematics, Vol. 343, No. 9 (2020), Art. 111965, 13 pp.
Abstract & Contents
Review from MathSciNet
Review from Zentralblatt
PDF
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A note on Nullstellensatz over finite fields, in:
Contributions in Algebra and Algebraic Geometry (Aurangabad, India, December 2017), S. G. Dani, S. K. Jain, J. K. Verma, and M. P. Wasadikar Eds.,
Contemporary Mathematics, Vol. 738,
American Mathematical Society, Providence,
RI, 2019, pp. 23-32.
Abstract & Contents
Review from MathSciNet
Review from Zentralblatt
PDF
- (with Peter Beelen and
Mrinmoy Datta)
Vanishing ideals of projective spaces over finite fields and a projective footprint bound,
Acta Mathematica Sinica (English Series), Vol. 35, No. 1 (2019), pp. 47-63.
Abstract & Contents
Review from MathSciNet
Review from Zentralblatt
PDF
- (with Jasbir S. Chahal)
Carlitz-Wan conjecture for permutation polynomials and Weil bound for curves over finite fields,
Finite Fields and Their Applications,
Vol. 54 (2018), pp. 366-375.
Abstract & Contents
Review from MathSciNet
Review from Zentralblatt
PDF
- (with Peter Beelen and
Mrinmoy Datta)
Maximum number of common zeros of homogeneous polynomials over finite fields,
Proceedings of the American Mathematical Society, Vol. 148, No. 4 (2018), pp. 1451-1468.
Abstract & Contents
Review from MathSciNet
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PDF
- (with Prasant Singh)
Minimum distance and the minimum weight codewords of Schubert codes,
Finite Fields and their Applications, Vol. 49 (2018), pp. 1-28.
Abstract & Contents
Review from MathSciNet
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PDF
- (with Yves Aubry,
Wouter Castryck,
Gilles Lachaud,
Michael E. O'Sullivan, and
Samrith Ram)
Hypersurfaces in weighted projective spaces over finite fields with applications to coding theory, Algebraic Geometry for Coding Theory and Cryptography
(IPAM, Los Angeles, CA, February 2016),
E. Howe, K. Lauter and J. Walker Eds.,
Association for Women in Mathematics Series,
Vol. 9,
Springer, New York, 2017, 37 pp.
Abstract & Contents
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PDF
- (with Mrinmoy Datta)
Remarks on Tsfasman-Boguslavsky conjecture and higher weights of
projective Reed-Muller codes,
Arithmetic, Geometry, Cryptography and Coding Theory
(Luminy, France, May 2015), A. Bassa, A. Couvreur and D. Kohel Eds.,
Contemporary Mathematics, Vol. 686,
American Mathematical Society, Providence,
RI, 2017, pp. 157--169.
Abstract & Contents
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PDF
- (with Mrinmoy Datta)
Number of solutions of systems of homogeneous polynomial equations over finite fields,
Proceedings of the American Mathematical Society, Vol. 145, No. 2 (2017), pp. 525-541.
Abstract & Contents
Review from MathSciNet
Review from Zentralblatt
PDF
- (with Mrinmoy Datta)
On a conjecture of Tsfasman and an inequality of Serre for the number of points on hypersurfaces over finite fields,
Dedicated to M. A. Tsfasman and S. Vlăduţ on their 60th birthdays,
Moscow Mathematical Journal, Vol. 15, No. 4 (2015), pp. 715-725.
Abstract & Contents
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PDF
- (with C. Krattenthaler) Computation of the a-invariant of ladder determinantal rings,
Dedicated to the memory of S. Abhyankar,
Journal of Algebra and Its Applications, Vol. 14, No. 9. (2015), Article 1540014, 24 pp.
Abstract & Contents
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PDF
- (with Peter Beelen and Sartaj Ul Hasan) Linear codes associated to determinantal varieties,
Discrete
Mathematics, Vol. 338 (2015), 1493-1500.
Abstract & Contents
Review from MathSciNet
Review from Zentralblatt
PDF
- (with Mrinmoy Datta)
Higher weights of affine Grassmann codes and their duals,
Algorithmic Arithmetic, Geometry, and Coding Theory
(Luminy, France, June 2013),
S. Ballet, M. Perret, and A. Zaytsev Eds.,
Contemporary Mathematics, Vol. 637,
American Mathematical Society, Providence, RI, 2015, pp. 79-91.
Abstract & Contents
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PDF
- (with B. Jonov and B.A. Sethuraman)
Hilbert series of certain jet schemes of determinantal varieties,
Pacific Journal of Mathematics, Vol. 272, No. 1 (2014), pp. 147-175.
Abstract & Contents
Review from MathSciNet
Review from Zentralblatt
PDF
- (with
Krishna Kaipa)
Automorphism groups of Grassmann codes,
Finite Fields and Their Applications,
Vol. 23 (2013), pp. 80-102.
Abstract & Contents
Review from MathSciNet
Review from Zentralblatt
PDF
PS
DVI
- (with Samrith Ram)
Arithmetic progressions in a unique factorization domain,
Acta Arithmetica, Vol. 54, No. 2 (2012), pp. 161-171.
Abstract & Contents
Review from MathSciNet
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PDF
PS
DVI
- (with Samrith Ram)
Enumeration of splitting subspaces over finite fields,
Arithmetic, Geometry, Cryptography and Coding Theory,
(Luminy, France, March 2011
),
Y. Aubry, C. Ritzenthaler, and A. Zykin Eds.,
Contemporary Mathematics, Vol. 574,
American Mathematical Society, Providence, RI, 2012, pp. 49-58.
Abstract & Contents
Review from MathSciNet
Review from Zentralblatt
PDF
PS
DVI
- (with Peter Beelen and
Tom Høholdt)
Duals of affine Grassmann codes and their relatives,
IEEE Transactions on Information Theory, Vol. 58, No. 6 (2012), pp. 3843-3855.
Abstract & Contents
Review from MathSciNet
PDF
PS
DVI
- (with
Samrith Ram)
Block companion Singer cycles, primitive recursive vector sequences, and coprime
polynomial pairs over finite fields,
Finite Fields and Their Applications,
Vol. 17, No. 5 (2011), pp. 461-472.
Abstract & Contents
Review from MathSciNet
Review from Zentralblatt
PDF
PS
DVI
- (with Mario Garcia-Armas and
Samrith Ram)
Relatively prime
polynomials and nonsingular Hankel matrices over finite fields,
Journal of Combinatorial Theory, Series A,
Vol. 118, No. 3 (2011), pp. 819-828.
Abstract & Contents
Review from MathSciNet
Review from Zentralblatt
PDF
PS
DVI
- (with Sartaj Ul Hasan
and Meena Kumari)
Primitive polynomials, Singer cycles, and word-oriented linear feedback shift registers,
Designs, Codes and Cryptography, Vol. 58, No. 2 (2011), pp. 123-134.
Abstract & Contents
Review from MathSciNet
Review from Zentralblatt
PDF
PS
DVI
- (with Peter Beelen and
Tom Høholdt)
Affine Grassmann codes,
IEEE Transactions on Information Theory, Vol. 56, No. 7 (2010), pp. 3166-3176.
Abstract & Contents
Review from MathSciNet
PDF
PS
DVI
- (with G. Lachaud)
Corrigenda and Addenda: Étale Cohomology, Lefschetz theorems and number of points of singular
varieties over finite fields,
Moscow Mathematical Journal, Vol. 9, No. 2 (2009), pp. 431-438.
Abstract & Contents
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PDF
-
(with A. R. Patil and H. K. Pillai)
Subclose families, threshold graphs, and the weight hierarchy of Grassmann and Schubert codes,
in: Arithmetic, Geometry, Cryptography and Coding Theory (Luminy, France, Nov 2007), G. Lachaud, C. Ritzenthaler, and M. Tsfasman Eds.,
Contemporary Mathematics, Vol. 487,
American Mathematical Society, Providence, RI, 2009, pp. 87-99.
Abstract & Contents
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PDF
PS
DVI
-
(with B. V. Limaye)
A geometric approach to saddle points of surfaces,
The Australian Mathematical Society Gazette, Vol. 36 (2009), No. 2, pp. 127-136.
Abstract & Contents
Review from MathSciNet
Review from Zentralblatt
PDF
PS
DVI
-
(with A. R. Patil and H. K. Pillai)
Decomposable subspaces, linear sections of Grassmann varieties, and higher weights of Grassmann codes,
Finite Fields and
their Applications, Vol. 15, No. 1 (2009), pp. 54-68.
Abstract & Contents
Review from MathSciNet
Review from Zentralblatt
PDF
PS
DVI
-
(with B. V. Limaye)
Sylvester's minorant criterion, Lagrange-Beltrami identity, and
nonnegative definitenes,
The Mathematics Student 2007, Special Centenary Volume (2008), pp. 123--130.
Abstract & Contents
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PDF
PS
DVI
-
(with K. N. Raghavan)
Hilbert functions of points on Schubert varieties in the Symplectic Grassmannian, Transactions of the American
Mathematical Society, Vol. 358, No. 12 (2006), pp. 5401-5423.
Abstract & Contents
Review from MathSciNet
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PDF
PS
DVI
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(with M. A. Tsfasman)
Schubert varieties, linear codes and enumerative combinatorics,
Finite Fields and their
Applications, Vol. 11, No. 4 (2005), pp. 684-699.
Abstract & Contents
Review from MathSciNet
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PDF
PS
DVI
-
(with C. Krattenthaler)
The Hilbert series of Pfaffian rings, in:
Algebra, Arithmetic and Geometry with Applications
(West Lafayette, 2000),
C. Christensen,
C. Bajaj,
G. Sundaram and
A. Sathaye Eds.,
Springer-Verlag, New York (2004),
pp. 337-356.
Abstract, Contents & Afternotes
Review from MathSciNet
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PDF
PS
DVI
-
(with M. A. Tsfasman)
Classical varieties, codes and combinatorics, in:
Formal Power Series and Algebraic
Combinatorics, (Vadstena, 2003) Actes/Proceedings,
K. Eriksson and
S. Linusson Eds.,
Linköping University, Sweden (2003), pp. 75-84.
Abstract & Contents
PDF
PS
DVI
- (with G. Lachaud)
Étale Cohomology, Lefschetz theorems and number of points of singular
varieties over finite fields,
Dedicated to Yuri I. Manin on the occasion of his 65th birthday,
Moscow Mathematical Journal, Vol. 2, No. 3 (2002), pp. 589-631.
Abstract & Contents
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PDF
PS
DVI
-
Hilbert functions of ladder determinantal varieties,
Discrete
Mathematics, Vol. 246 (2002), pp. 131-175.
Abstract & Contents
Review from MathSciNet
Review from Zentralblatt
PDF
PS
DVI
- (with G. Lachaud)
Number of solutions of equations over finite fields,
and a conjecture of Lang and Weil,
in:
Number Theory and Discrete
Mathematics
(Chandigarh, 2000),
A. K. Agarwal,
B. Berndt,
C. Krattenthaler,
G. L. Mullen, K Ramachandra
and M. Waldschmidt Eds.,
Trends in
Mathematics, Birkhäuser,
Basel (2002), pp. 269-291.[Published in India by
Hindustan Book Agency, New Delhi,
2002.]
Abstract & Contents
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PDF
PS
DVI
- (with G. Lachaud)
Hyperplane sections of Grassmannians and the
number of MDS linear codes,
Finite Fields and their
Applications, Vol. 7, No. 4 (2001), pp. 468-506.
Abstract & Contents
Review from
MathSciNet
Review from Zentralblatt
PDF
PS
DVI
-
A note on Hodge's postulation formula for Schubert varieties,
in:
Geometric
and Combinatorial Aspects of Commutative Algebra (Messina, 1999),
J. Herzog and
G. Restuccia Eds.,
Lecture Notes in Pure and Applied Mathematics, Vol. 217,
Marcel Dekker, New York (2001), pp. 211-220.
Abstract & Contents
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PDF
PS
DVI
- (with G. Lachaud)
Higher weights of Grassmann codes, in:
Coding Theory,
Cryptography and Related Areas
(Guanajuato, 1998),
J. Buchmann,
T. Hoeholdt,
H. Stichtenoth and H. Tapia-Recillas Eds.,
Springer-Verlag,
Berlin (2000), pp. 122-131.
Abstract, Contents & Afternotes
Review from MathSciNet
Review from Zentralblatt
PDF
PS
DVI
- On the enumeration of indexed monomials and the computation of
Hilbert functions of ladder determinantal varieties, in:
Formal Power Series and Algebraic
Combinatorics, (Barcelona, 1999) Actes/Proceedings,
C. Martinez, M. Noy and O. Serra Eds., Universitat Politecnica de
Catalunya, Spain (1999), pp. 225-232.
Abstract
PDF
PS
DVI
- Young bitableaux, lattice paths and Hilbert functions,
Journal
of Statistical Planning and Inference (Special issue on
Lattice Path Combinatorics and Applications), Vol. 54 (1996), pp. 55-66.
Abstract
Review from MathSciNet
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PDF
PS
- Young multitableaux and higher dimensional determinants,
Advances in Mathematics, Vol. 121, No. 2 (1996), pp. 167-195.
Review from MathSciNet
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PDF
PS
- (with G. Lachaud)
Grassmannians over finite fields and MDS Codes,
Proceedings of the Discussion Meeting on Cryptography and Computation,
(Coordinators: C. E. Veni Madhavan and R. Balasubramanian),
Jawaharlal Nehru Centre for Advanced
Scientific Research,
Bangalore, 1995, 4 pages.
PDF
PS
- Abhyankar's work on Young tableaux and some recent developments,
in: Algebraic Geometry and its Applications (West Lafayette, IN, 1990),
C. Bajaj Ed.,
Springer-Verlag, New York,
(1994), pp. 233-265.
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PS
- (with S. S.
Abhyankar) Young tableaux and linear independence of
standard monomials in multiminors of a multimatrix,
Discrete
Mathematics,, Vol 96 (1991), pp. 1-32.
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PDF
- (with M. V. Deshpande) Algebraic characterization of compact
abelian groups, American
Mathematical Monthly, Vol. 98, No. 3 (1991), pp. 235-237.
Review from MathSciNet
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PS
Obituary and Foreword
- Remembering Shreeram S. Abhyankar,
(with appendices by A. Sathaye, B. Singh, S. D. Cutkosky, and R. V. Gurjar),
Asia Pacific Mathematics Newsletter, Vol. 3, No. 1 (2013), pp. 22-30.
[This article is also reprinted, with permission from the APMN, in
Resonance Vol. 18, No. 5 (2013), pp. 397-411, and the
RMS Mathematics Newsletter, Vol. 23 , No. 4 (2013), pp. 271-279. ]
PDF (APMN)
PDF (Resonance)
PDF (RMS-ML)
- (with A. Sathaye), Foreword to the Special Issue in Honor of Shreeram S. Abhyankar,
Journal of Algebra and its Applications,
Vol. 14, No. 9 (2015), Article 1502001, 4 pp.
PDF
Expository Articles
- Discriminants in Algebra and Arithmetic,
Bona
Mathematica, Vol. 11, No. 2-3 (2000),
pp. 43-62.
[This article is also reprinted in the Bulletin of the Bombay Mathematical
Colloquium, Vol. 15, No. 1-2 (1999*), pp. 33-47 with permission from the
Editor of Bona Mathematica. *: date of actual publication: Jan 2001.]
Abstract & Contents
PDF
PS
DVI
Articles on Pedagogy and History
-
Teaching Calculus using Internet: Some Experiments and Experiences, in:
Science, Technology and Mathematics Education for Human Development,
Proceedings of the CASTME-UNESCO-HBCSE International Conference
(Goa, Feb. 2001),
Vol. 1, Eds., S. C. Agarkar and V. D. Lale ,
Homi Bhabha Centre for
Science Education,
Tata Institute of Fundamental Research,
Mumbai, 2002, pp. 219-223.
[Article as a PDF file]
[Article in HTML format]
[Article as a MS Word File]
Related News Item: Tribune India (July 2001),
-
Effective Teaching and Modern Perspectives in Mathematics, Souvenir of the
Mathematics Association,
IIT Bombay, 2002, pp. 37-42.
[This article is a slightly revised version of the text of an invited talk at
the CEP Course on Effective
Teaching for Technical Teachers, Department of
Humanities and Social Sciences, IIT Bombay, January 1996.]
[Article as a PDF file]
[Article as a PS file]
-
The role of history in learning and teaching mathematics: A personal perspective, IMS-2018 Presidential Address (General), The Mathematics Student. Vol. 88, No. 1-2 (2019), pp. 27-35. [This article is also reprinted in ICCM Notices, Vol. 8, No. 2 (2020), pp. 49-53, with permission from the editor of The Mathematics Student.]
[Article as a PDF file] [Article in Math Student] [Article in ICCM Notices]
Lecture Notes
See here.
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