Sample publications:

(with K Ono, A Singh) MacMahon's sums-of-divisors and allied $q$-series, preprint. New!

(with G E Andrews, R Tauraso) Extensions of MacMahon's sums of divisors, preprint. New!

(with S Wagner) The MacMahon $q$-Catalan is convex, accepted. Annals of Combinatorics.

(with D Callan) Gaussian inequality, accepted. Rocky Mountain J. Math.

(with V H Moll) Infinite logconvexity, accepted. Online Journal of Analytic Combinatorics.

(with V H Moll, J L Santander, K Mclaughlin, C Koutschan) Collisionless shock region of the KdV equation, Physica D: Nonlinear Phenomena, 456 (2023).

(with C Koutschan, D Zeilberger) Yay for determinants! A revised version appeared, with a different title in Séminaire Lotharingien de Combinatoire, B89a (2023).

(with W Marszalek) SIB in multiple transonic crossings of unsteady gravitational flows, Physics Letters A, V. 477 (2023).

(with G E Andrews, C Ballantine) Hook length and symplectic content in partitions, J. Combinatorial Theory, Series A 200 (2023).

(with G E Andrews, C Ballantine) Refinements of Beck-type partition identities, Discrete Math. 345, no. 12, Paper No. 113110, (2022).

(with D Zeilberger) An elegant Multi-Integral that implies an identity of Dougherty and McCammond. Palestine J. of Mathematics, Vol. 11 #4 (2022).

(with G Comert, N Begashaw, N G. Medhin, M Chowdhury) Estimating the queue lengths from probe vehicles at traffic signals, Submitted.

  • Theorems, problems and conjectures, preprint. (updated, 25 August, 2022)

    (with A Duncan, V H Moll, V Sharma) Filter integrals for orthogonal polynomials, Hardy-Ramanujan Journal 44 (2021), 116-135.

    (with V H Moll, V Sharma, D Villamizar) Arithmetic properties of the sum of divisors, J. Number Theory, Vol. 223, June 2021, Pages 325-349.

  • (with V H Moll, A Straub, C Vignat) A triple integral analog of a multiple zeta value, International J Number Theory, Vol. 17, No. 02, pp. 223-237 (2021).

    (with M Glasser, M Jones, V Moll, R Posey, D Varela) The Cauchy-Schlomilch transformation, Integral Transforms Spec. Funct. 30 (2019), no. 12, 940-961.

    (with R Tauraso) A congruence for a double harmonic sum, Scientia, Ser. A, Math. Sci. (N.S.) 29, 37-44 (2019).

    (with D Callan, H Ohtsuka and R Tauraso) Revitalized automatic proofs: demonstrations, INTEGERS, 17 (2017), Axx.

    (with R Tauraso) Two Triple binomial sum supercongruences (including abelian squares) Journal of Number Theory, 175 (2017), 140-157.

    (with X Guan, L Jiu, V H Moll and C Vignat) A series involving Catalan numbers: Proofs and demonstrations, Elemente der Mathematik, V 71, 2016.

    (with R Tauraso) Supercongruences for the Almkvist-Zudilin numbers, Acta Arithmetica, 11 May 2016 (online).

    Explicit computations with the Divided Symmetrization operator, Proc. Amer. Math. Soc., V 144, #7, 2016.

  • (with M. Apagodu, D Zeilberger) Wilf's ``Snake Oil" Method Proves an Identity in The Motzkin Triangle, preprint.

    (with W Marszalek) Memristive Jounce (Newtonian) Circuits, J Applied Mathematical Modelling, V 40, #4, 2016.

    (with W Marszalek) Least action principle for mem-elements, J circuits, systems & computers, V 24, #10, 2015. Follow the link for this current topic.

    (with E Leven) Multi-cores, posets, and lattice paths, Advances in Appl. Math., Vol 71, 2015, pp 1-13.

    (with V Moll) Involutions and their progenies, J of Combinatorics, Vol 6, #4, 2015.

    (with M B Can, M Jensen) Divisors and specializations of Lucas polynomials, J of Combinatorics, Vol 6, #1-2, 2015.

    (with X Chen, V Moll, B Sagan) Generalized Fibonacci polynomials and Fibonomial coefficients, Annals of Combinatorics, V 18, 2014, pp 541-562.

    (with A Dixit, X Guan, L Jiu, V Moll) Unimodality of polynomials from rational integral: proof revisited, J Math Anal & Appl., V 420, 2014, pp 1154-1166.

    (with V. De Angelis, A. Dixit, V Moll, C. Vignat) From sequences to polynomials via operator orderings, J. Mathematical Physics, V 54, 2013.

    (with D Callan, V H Moll) p-adic analysis and combinatorics of truncated exponential sums, J INTEGERS, Vol 13, paper A21, 2013.

    (with V H Moll, C Vignat) A probabilistic interpretation of a sequence related to Narayana polynomials, OnLine J Combinatorics, V 8, #3, 2013.

    (with D Borwein, J Borwein, A Straub) Normalizing factor in a q-Dirac delta, J Mathematical Physics, V.53, #7, 2012.

  • (with V H Moll, V G Papanicolaou) A family of palindromic polynomials, Scientia, Series A: Math. Sciences 24, 2013, pp. 25-32.

    (with O Espinosa, I Gonzalez, M Harrison, V H Moll, A Straub) On Ramanujan's Master Theorem, (online 1st) The Ramanujan J, 11 Jan. 2012.

    (with V De Angelis, V H Moll) Complementary Bell numbers: Wilf's conjecture, Advances in Combinatorics, 2013, pp 23-56

    Differential operators, shifted parts, and hook lengths, The Ramanujan J, Vol 24, #3, 2011. Follow the link for background material.

  • (with S B Ekhad) Play time with determinants, (unpublication)
  • (with M Can, V H Moll) Broken bracelets, Molien series, paraffin wax and an elliptic curve of conductor 48, SIAM J. Discrete Math. V.25, #4, 2011, pp.1843-1859. (warning: large file).

    (V de Angelis, M Lin, V H Moll, B Sury) A binomial identity, Elemente der Mathematik, V.67, #1, 2012, pp.18-25.

    (with V H Moll, C Vignat) A quartic integral a la Schwinger, Schur and Bessel, The Ramanujan J, V.28, #1, 2012.

    (with V H Moll) Arithmetic properties of plane partitions in a hypercube, Elec. J. Combin., V.18, #R1, 2011.

    (with C Koutschan, V H Moll, E Rowland) The iterated integrals of ln(1+x^n), Inter. J. Number Theory, V.8, #1, 2012.

    (with V H Moll) A by-product of an integral evaluation, The Ramanujan J, V 37, 2015, pp 219-222.

    (with L Medina, V Moll) Gems in Experimental Mathematics, this book is V.517, AMS Contemporary Math, July 2010.

    (with Coffey, Espinosa, Koutschan, Manna, Moll) Integrals of powers of loggamma, Proc. Amer. Math. Soc., #139, 2011.

    (with O Espinosa, V Moll, A Straub) Wallis-Ramanujan-Schur-Feynman, Amer. Math. Monthly, August/Sept., 2010.

    A note on a question due to A. Garsia, , in Contemporary Mathematics, V.517, July 2010.

    (with V Moll, A Straub) One-loop correction integrals for orthopositronium lifetimes in QED, J Math. Physics, #50, 2009.

    (with G Heinig) Is every complex matrix similar to a Toeplitz matrix? Birkhauser, V.199, Jan. 2010. In memoriam, Georg Heinig, a wonderful Mensch!

    (with R P Stanley) Polynomial coefficient enumeration, preprint.

    A note on Fibonacci-type polynomials, J. of INTEGERS, #A2, 10 (2010).

    (with A. Straub, V.H. Moll) Valuation of k-binomial coefficients, Acta Arithmetica, #149, 2009, 31-42.

    (with V H Moll) Tapas in Experimental Mathematics - this book is V. 457, AMS Contemporary Math, 2008. (type "amdeberhan" under Quick Search)

    (with V.H. Moll) A dozen integrals: Russell-style Math Newsletter, Ramanujan Math Soc, Vol 18, #1 June 2008.

    (with L. Medina, V.H. Moll) p-adic asymptotic analysis. Proc. Amer. Math. Soc., v.137, #3, March 2009.

    (with O. Espinosa, V.H. Moll) Laplace transform of the digamma function: integral due to Glasser-Manna-Oloa, Proc. Amer. Math. Soc., 136 (2008).

    Integrals in Gradshteyn & Ryzhik: Part 5 and Part 7 and Part 9 and Entry 3.411.5.

    (with D. Zeilberger) "Trivializing" generalizations of some Izergin-Korepin-type determinants. Discrete Math. & Theor. Comp. Sci. 9 (2007), Nancy, France.

    (with L. Medina, V.H.Moll) A dynamical system of arctangent sequence, Jour. Number Theory, 128 (2008).

    (with V.H.Moll) A formula for quartic integral: old and new proofs. The Ramanujan Journal, Oct. 2007.

    (with V.H.Moll, D. Manna) 2-adic valuation of Stirling Numbers Vol. 17, #1, 2008, Experimental Mathematics.

    (with V.H.Moll, D. Manna) 2-adic valuations arising from rational integral J. Combin. Theory Ser. A, Vol. 115, #8, 2008.

    Umemura polynomials associated to Painleve III also available at Physics Letters A 354 (2006)

    (with A. Ayyer) Towards the moduli space of extended partial isometries

  • (with M. Bona, B.E. Sagan) Double log-concavity. --- under construction.
  • (with W. Marszalek, R. Riaza) Singularity crossing phenomena in DAEs: a 2-phase fluid flow appl. case study. Int. J. Comp. Math. Appl., (49) 2-3, 2005.

    Cylindrically symmetric solution approaching Einstein's Universe. J. Geometry & Topology, vol. 2, (3) 2002.

  • Traveling wave DAEs in spray dynamics, has been presented -- Vancouver, CA, minisymposium Aug, 2001
  • Two Symmetry Problems in Potential Theory. June 6, 2001.

    (with D. Zeilberger) Determinants Through The Looking Glass. Its companion Maple package is: DODGSON. Adv. Appl. Math., (27) #2/3, 2001 (special issue.)
    A brief commentary for the general reader at: Online MAA.

    A Determinant of the Chudnovskys: Generalizing the Elliptic Frobenius- Stickelberger-Cauchy Determinantal Identity. (Elec. J. Comb. 2000.)

    (with D. Zeilberger) q-Apery Irrationality Proofs by q-WZ Pairs.

    (with D. Zeilberger) Hypergeometric Series Acceleration via the WZ Method.

    (with S.B. Ekhad) A Condensed Condensation Proof of a Determinant Evaluation Conjectured by Greg Kuperberg and Jim Propp.

    (with G. Porru, S.Vernier-Piro) Maximum principles for a class of nonlinear 2nd order elliptic PDEs.

    (with M. Zeleke) On Injectivity of Combinatorial Radon Transform of Order Five.

    Faster and Faster convergent series for Zeta(3).

    An integral inequality for a class of elliptic operators of 4th order, Rendiconti Seminario Fac Sc., Univ Cagl, Vol 60, #2: MR 92k 35078.

    (with G.Porru) Integral inequalities for linear elliptic operators of 2nd order, Ricerche di Matematica, Napoli, Vol XXXVII #1: MR 90k 35045.

    (with G.Heinig) On the inverses of Hankel & Toeplitz Mosaic matrices, Seminar Analysis, Academic-Verlag, Berlin: MR 90j 15007.

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