Publications

 

Here is a complete list of my research articles. The list of papers up to end of 2005 is also available in pdf. The postscript, tex or latex files of some of the newer papers below are available where highlighted.

A few of the older tex files may require as input macros (save with the name macros.m) or pre (save as pre.sty).

Recent Articles and New Additions

• A Knopfmacher, A Odlyzko, B Pittel, B Richmond, D Stark, G Szekeres and N Wormald, ``On set partitions with unequal block sizes'', {\it Electronic J. Combinatorics {\bf 6}, (1999), article R2.
• A Knopfmacher and M E Mays, ``The sum of distinct parts in compositions and partitions'', {\it Bull. Inst. Comb. \& Appl. {\bf 25}} (1999), 66-78.
• A Knopfmacher, ``On the degrees of irreducible factors of polynomials over a finite field'', {\it Discrete Mathematics {\bf 196}} (1999), 197-206.
• A Knopfmacher and J Knopfmacher, ``Arithmetical semigroups related to trees and polyhedra'', {\it Journal of Combinatorial Theory, Series A {\bf 86} (1999), 85-102.
• A Knopfmacher and M E Mays, ``Compositions with m distinct parts'', {\it Ars Combinatorica {\bf 53} (1999), 111-128.
• A Knopfmacher and N Robbins, ``Some arithmetic properties of Eulerian numbers'', {\it J. Comb. Math. \& Comb. Computing} {\bf 36} (2001), 31-42.
• G Andrews, A Knopfmacher and J Knopfmacher,``Engel Expansions and the Rogers-Ramanujan Identities'', {\it Journal of Number Theory {\bf 80}} (2000),273-290.
• G Andrews, A Knopfmacher and P Paule, ``An Infinite Family of Engel Expansions of Rogers-Ramanujan Type'', {\it Advances in Applied Math. {\bf 25}} (2000), 2--11.
• A Knopfmacher and M E Mays, ``Graphical Compositions I: Basic Enumeration''. {\it Integers {\bf 1}} (2001), article A4.
• A Knopfmacher, M E Mays and J N Ridley, ``Graphical Compositions in Mathematica''. Graph Composition Pictures
• G Andrews and A Knopfmacher, ``An algorithmic approach to discovering and proving q-series identities'',{\it Algorithmica {\bf 29}} (2001), 34-43.
• A Knopfmacher and H. Prodinger, ``Combinatorics of geometrically distributed random variables: Value and position of the $r$th left-to-right maximum'' , {\it Discrete Math. {\bf 226}} (2001), 255-267.
• A Knopfmacher and H. Prodinger,``A simple card guessing game revisited'', {\it Elec. J. Comb.} {\bf 8(2)} (2001), article R13.
• G Andrews, A Knopfmacher, P Paule and B Zimmermann,``Engel expansions of q-series by computer algebra'', {\it Symbolic computation, number theory, special functions, physics and combinatorics} (Gainesville, FL, 1999), 33--57, Dev. Math., 4, Kluwer Acad. Publ., Dordrecht, 2001.
• A Knopfmacher, ``John Knopfmacher - Mathematical and other memories'', {\it Notices of S. A. Math. Soc. {\bf 31}} (2000), 11-15.
• A Knopfmacher and D S Lubinsky, `` Mathematica Evidence that Ramanujan kills Baker-Gammel-Wills'', {\it Applied Maths and Computation {\bf{128}} (2002), 289-302.
• P Grabner, A Knopfmacher and H. Prodinger, ``Combinatorics of geometrically distributed random variables: Run statistics" {\it Theoret. Comp. Sci.} {\bf 297} (2003), 261--270.
• P Grabner and A Knopfmacher ``Arithmetic and Metric Properties of $p$-Adic Engel Series Expansions'', Publicationes Mathematicae Debrecen 63 (2003), 363--377.
• A Knopfmacher and N Robbins,``On Binary and Fibonacci Compositions'', {\it Annales Univ. Sci. Budapest., Sect. Comp. {\bf 22}} (2003), 193-206.
• A Knopfmacher and N Robbins,``On Pell Partitions'', {\it The Fibonacci Quarterly { \bf 42}} (2004), 348--352.
• A Knopfmacher and H. Prodinger, `` Descents in geometrically distributed random variables'', Mathematics and Computer Science: Algorithms, Trees, Combinatorics and Probabilities, Drmota, Flajolet, Gardy and Gittenberger (Eds.) (2004), 339--350.
• J von zur Gathen, A Knopfmacher, F Luca, L Lucht and I Shparlinski,``The average order in cyclic groups'', {\it J. Theorie de Nombres Bordeaux {\bf 16}} (2004), 107--124.
• P Hitczenko and A Knopfmacher`` Gap-free compositions and gap-free samples of geometric random variables'' {\it Discrete Math. {\bf 294}} (2005), 225--239.
• A Knopfmacher and N Robbins,``Compositions with parts constrained by the leading summand'', to appear in {\it Ars Combinatoria}.
• A Knopfmacher and N Robbins,``Identities for the total number of parts in partitions of integers'', to appear in {\it Utilitas Mathematica}.
• M Archibald, A Knopfmacher and H Prodinger,`` The number of distinct values in a geometrically distributed sample'' to appear in {\it European Journal of Combinatorics}.
• A Knopfmacher and M E Mays ``Ordered and unordered factorizations of integers'', to appear in {\it The Mathematica Journal}.
• C Brennan and A Knopfmacher ``The distribution of ascents of size $d$ or more in samples of geometric random variables", to appear in {\it Discrete Math. and Th. Comp. Sci.}, (Proceedings of AofA 2005).
• A Knopfmacher and N Robbins,``On multi-color partitions with distinct parts'', to appear in {\it Ars Combinatoria}.
• A Knopfmacher and M E Mays ``A survey of factorization counting functions''.
• G Andrews, A Knopfmacher and B Zimmermann, ``On the number of distinct values of multinomial coefficients''.
• A Knopfmacher and M E Mays ``Dirichlet generating functions and factorization Identities''. to appear in {\it Congressus Numerantum}.
• P Grabner and A Knopfmacher ``Analysis of some new partition statistics''to appear in {\it The Ramanujan Journal}.

Pre-publication versions of papers from the special issue of QUAESTIONES MATHEMATICAE dedicated to John Knopfmacher can be found here.

Publication List 1992 - 1998

• A Knopfmacher and J Knopfmacher,``Infinite series expansions for p-adic numbers'', {\it Journal of Number Theory {\bf41}} (1992), 131-145.
• A Knopfmacher, ``Elementary properties of the subtractive Euclidean algorithm'', {\it Fibonacci Quarterly {\bf 30}} (1992) , 80-83.
• K-H Indlekofer, A Knopfmacher and J Knopfmacher, ``Alternating Balkema-Oppenheim expansions of real numbers'', {\it Bulletin of the Belgian Math. Soc.{\bf 44}} (1992), 17-28.
• A Knopfmacher, J Knopfmacher and R Warlimont, ``Factorisatio Numerorum in arithmetical semigroups'', {\it Acta Arithmetica {\bf61}} (1992), 327-336.
• A Knopfmacher and J Knopfmacher,``Metric properties of algorithms inducing Luroth series expansions of Laurent series'', {\it Asterisque {\bf209}} (1992), 237-246.
• A Knopfmacher, J Knopfmacher and R Warlimont, ``Ordered factorizations for integers and arithmetical semigroups'', {\it Advances in Number Theory},(F Gouvea and N Yui,eds),Oxford University Press (1993),151-165.
• A Knopfmacher, ``Rational numbers with predictable Engel product expansions'', in {\it Applications of Fibonacci Numbers {\bf5}} (G E Bergum et al eds.), Kluwer 1993, 421-427.
• A Knopfmacher and J Knopfmacher, ``Counting irreducible factors of polynomials over a finite field'', {\it Discrete Mathematics {\bf 112}} (1993), 103-118.
• A Knopfmacher and J N Ridley, ``Reciprocal sums over partitions and compositions'', {\it SIAM J. Discrete Math. {\bf 6}} (1993),388-399.
• H Gingold,A Knopfmacher and D S Lubinsky, ``The zero distribution of the partial products of power product expansions'', {\it Analysis {\bf 13 }} (1993), 133-157.
• H Buchanan, A Knopfmacher and M E Mays,``On the cyclotomic identity and related product expansions'', {\it Australasian J. of Combinatorics {\bf 8}} (1993) , 233-245.
• A Knopfmacher, J Knopfmacher and R Warlimont,`` Lengths of factorizations for polynomials over a finite field'', {\it Contemporary Math. {\bf168}} (1994) , 185-206.
• B Richmond and A Knopfmacher ,``Compositions with distinct parts'', {\it Aequationes Math. {\bf 49}} (1995), 86-97.
• A Knopfmacher and M E Mays,``Pierce expansions of ratios of Fibonacci and Lucas numbers and polynomials'', {\it Fibonacci Quarterly {\bf 33}} (1995), 153-163.
• A Knopfmacher and R Warlimont, ``Distinct degree factorizations for polynomials over a finite field'', {\it Trans. Amer. Math. Soc. {\bf 347}} (1995), 2235-2243.
• H Gingold and A Knopfmacher, ``Analytic properties of power product expansions'', {\it Canadian J. of Math. {\bf 47}} (1995), 1219-1239.
• A Knopfmacher and R Warlimont, ``Distinct degree factorizations in arithmetical semigroups'', {\it Manuscripta Math. {\bf 87}} (1995), 481-487.
• A Knopfmacher and H.Prodinger, ``Explicit and asymptotic formulae for the expected values of the order statistics of the Cantor distribution'', {\it Statistics and Prob. Lett. {\bf 27} } (1996), 189-194.
• A Knopfmacher and R Warlimont, ``Counting permutations and polynomials with a restricted factorization pattern'', {\it Australasian J. of Combinatorics {\bf 13}} (1996), 151-162.
• A Knopfmacher and J Knopfmacher, ``Metric properties of some special p-adic series expansions'',{\it Acta Arithmetica {\bf 76}} (1996), 11-19.
• A Knopfmacher and R Warlimont, ``Covers of finite sets with distinct block sizes'', {\it Ars Combinatorica {\bf 44}} (1996), 193-203.
• A Knopfmacher and E Manstavicius,``On the largest degree of an irreducible factor of a polynomial in $\F_q[x]$'', {Lietuvos Matematikos Rinkinys {\bf 37}} (1997), 50-60.
• P J Grabner and A Knopfmacher,``Metric properties of Engel series expansions of Laurent series'', {\it Math. Slovaca {\bf 48}} (1998), 233-243.
• A Knopfmacher and H Prodinger, ``On Carlitz compositions'', {\it European J. of Combinatorics {\bf 19}} (1998), 579-589.

A Knopfmacher, G Mullen and J N Ridley,``Irreducible polynomials over finite fields and nets'', {\it App. Alg. Eng. Com. Comp. {\bf 9}} (1998), 265-269.

EXPOSITORY ARTICLES

• A Knopfmacher, ``New representations for power series via infinite series and products''. {\it S.A. Journal of Science {\bf 85}} (1989), 89-90.
• A Knopfmacher, ``Enumerating basic properties of polynomials over a finite fields'', {\it S.A. Journal of Science {\bf 91}} (1995), 10-11.
• P Grabner, A Knopfmacher and H. Prodinger, ``Run statistics for geometrically distributed random variables", Proceedings of LATIN'2000, {\it Lecture Notes in Comp. Sci. {\bf 1776}}, Gonnet, Panario and Viola (Eds.), 457-462.

Publication List 1986 - 1991

• A Knopfmacher,``Positive Convergent Approximation Operators associated with Orthogonal Polynomials for weights on the whole real line", {\it J. Approx. Theory} {\bf 46} (1986) 182-203.
• A Knopfmacher and D.S. Lubinsky, ``Mean Convergence of Lagrange interpolation for Freud's weights with application to product integration rules", {\it J. Comp. and Appl. Math}. {\bf 17} (1987) 79-103.
• A Knopfmacher and J. Knopfmacher, ``A new construction of the real numbers (via infinite products)", {\it Nieuw Arch. Wisk.},{\bf 5}, no. 1 (1987); 19-31.
• A Knopfmacher and J. Knopfmacher, ``A new infinite product representation for real numbers", {\it Monatshefte Math}, {\bf 104} (1987) 29-44.
• A Knopfmacher, ``Pointwise convergence of Lagrange interpolation based at the zeros of orthonormal polynomials with respect to weights on the whole real line", {\it J. Approx. Th.}, {\bf 51} no. 3 (1987); 231-253.
• A Knopfmacher and D.S. Lubinsky, ``Analogues of Freud's conjecture for Erd\'os type weights and related Polynomial Approximation problems", in Approximation Theory, Tampa (E.B. Saff ed), Lect. Notes Math., Vol.1287, Springer-Verlag (1987), Berlin 21-69.
• A Knopfmacher and J. Knopfmacher, ``Infinite series representations for complex numbers", {\it Rendiconti Circolo Mat. Palermo, {\bf 36}} (1987) 434-456.
• A Knopfmacher, D.S. Lubinsky and P. Nevai, ``Freud's conjecture and approximation of reciprocals of weights by polynomials", {\it Constructive Approximation}, {\bf 4}, no. 1 (1988); 9-20.
• A Knopfmacher and J. Knopfmacher, ``Two concrete new constructions of the real numbers", {\it Rocky Mtn. J. Maths}, {\bf 18},(1988), 813-824.
• A Knopfmacher and J Knopfmacher, ``The exact length of the Euclidean algorithm in $\F_{\!\!q}[X]$'', {\it Mathematika {\bf 35}} (1988), 297-304.
• A Knopfmacher and D.S. Lubinsky, ``Asymptotic Behaviour of the ratio of Christoffel functions for weights $W^2$ and $W^2g$", {\it J. Approx. Th.} {\bf 52} (1988) 293-314.
• A Knopfmacher and J. Knopfmacher, ``Inverse polynomial expansions of Laurent series", {\it Constr. Approx.}, {\bf 4} (1988) 379-389.
• A Knopfmacher and J. Knopfmacher, ``A product representation for power series", {\it Complex Variables {\bf 10}} (1988); 283-294.
• A Knopfmacher and J. Knopfmacher, ``A product expansion in P-ADIC and other non-archimedean fields", {\it Proc. Amer. Math. Soc. {\bf 104}} (1988), 1031-1035.
• A Knopfmacher and J. Knopfmacher, ``Representations for real numbers via k-th powers of integers", {\it Fibonacci Quarterly} {\bf 27} (1989), 49-60.
• A Knopfmacher and J. Knopfmacher, ``Infinite products for power series", {\it J. Approx. Theory {\bf 59}} (1989), 276-281.
• A Knopfmacher, ``Infinite product representations in complex quadratic fields'', {\it Portugaliae Mathematica} {\bf 46} (1989), 365-383.
• A Knopfmacher and J Knopfmacher, ``A binomial product representation for p-adic numbers'', {\it Arch. Math. {\bf 52}} (1989), 333-336.
• A Knopfmacher and J Knopfmacher, ``Two constructions of the real numbers via alternating series'', {\it Int. J. Math. \& Math. Sci. {\bf 12}} (1989) 603-613.
• A Knopfmacher and J. Knopfmacher, ``Series expansions in p-adic and other non-archimedean fields'', {\it Journal of Number Theory. {\bf 32}} (1989), 297-306.
• A Knopfmacher and J Knopfmacher, ``P-adic and non-archimedean product representations'', {\it Results in Mathematics {\bf 15}} (1989), 324-334.
• A Knopfmacher and J Knopfmacher, ``Inverse polynomial expansions of Laurent Series II'', {\it J. Comp. and App. Math} {\bf 28} (1989), 249-257.
• A Knopfmacher, ``A radix product representation for real numbers'', {\it Fibonacci Quarterly {\bf 28}} (1990), 290-297.
• A Knopfmacher and J Knopfmacher, ``Maximum length of the Euclidean algorithm and continued fraction in $F(x)$'', in {\it Applications of Fibonacci Numbers} (G. E. Bergum et al eds.), Kluwer 1990, 217-222.
• A Knopfmacher and J Knopfmacher, ``An alternating product representation for real numbers'', in {\it Applications of Fibonacci Numbers} (G.E. Bergum et al eds.), Kluwer 1990, 209-216.
• A Knopfmacher, J Knopfmacher and J N Ridley, ``Unique factorizations of formal power series'', {\it J. Math. Anal. and Applic. {\bf 149}} (1990), 402-411.
• S Kalpazidou, A Knopfmacher and J Knopfmacher, ``L\"uroth-type alternating series representations for real numbers'', {\it Acta Arithmetica {\bf 55}} (1990) ,311-322.
• A Knopfmacher and J Knopfmacher, ``Counting polynomials with a given number of zeros in a finite field'', {\it Linear and Multilinear Algebra} {\bf 26} (1990), 287-292.
• A Knopfmacher and J Knopfmacher,``The distribution of values of polynomials over a finite field'', {\it Linear Algebra and Applications {\bf 134}} (1990), 145-151.
• A Knopfmacher and J Knopfmacher, ``Normality of some p-adic product expansions", {\it J. Australian Math. Soc. Series A {\bf49}} (1990),258-263.
• A Knopfmacher and D S Lubinsky, ``Non-normality of continued fraction partial quotients modulo $q$'', {\it Rev. Colombiana Mat. {\bf24}} (1990), 179-182.
• A Knopfmacher, ``Generalized series expanions of functions'', in Progress in Approximation Theory (Nevai,Pinkus eds.),Academic Press (1991), 513-533.
• A Knopfmacher, ``The length of the continued fraction expansion for a class of rational functions in $\F_{\!\!q}(X)$'', {\it Proc. Edinburgh Math. Soc. {\bf34}} (1991), 7-17.
• A Knopfmacher, ``Infinite product factorizations of analytic functions'', {\it J. Math. Anal. \& Applic. {\bf162}} (1991), 526-536.
• S Kalpazidou, A Knopfmacher and J Knopfmacher, ``Metric properties of alternating Luroth series'', {\it Portugaliae Mathematica {\bf 48}} (1991), 319-325.
• A Knopfmacher and J Knopfmacher,``The number of steps in the Euclidean algorithm over complex quadratic fields'', {\it BIT {\bf 31}} (1991), 286-292.
• A Knopfmacher and L Lucht, ``The radius of convergence of power product expansions'', {\it Analysis {\bf11}} (1991), 91-99.

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