Publications

Johann Cigler

 

Books

[A] Einführung in die lineare Algebra und Geometrie I,

Manz Verlag, Wien 1976.

[B] Einführung in die lineare Algebra und Geometrie II,

Manz Verlag, Wien 1977.

[C] Einführung in die Differential- und Integralrechnung I,

Manz Verlag, Wien 1978.

[D] Einführung in die Differential- und Integralrechnung II,

Manz Verlag, Wien 1978.

[E] (gem. m. H.C. Reichel) Topologie,

B.I. Hochschultaschenbücher 121,1978.

[F] (Gem. m. V.Losert u. P.Michor) Banach modules and functors on categories of Banach spaces,

Lecture Notes in Pure and Applied Math. 46 , M. Dekker 1979.

[G] Grundideen der Mathematik,

Math. Texte 5, B.I. 1992.

[H] Körper – Ringe - Gleichungen,

Spektrum 1995.

 

Papers

 

[1] Asymptotische Verteilung reeller Zahlen mod 1,

Mh. Math. 64 (1960), 201-225.

[2] Der individuelle Ergodensatz in der Theorie der Gleichverteilung mod 1,

J. reine angew. Math. 205 (1960), 91-100.

[3] Ziffernverteilung in theta - adischen Brüchen,

Math. Zeitschrift 75 (1961), 8-13.

[4] Hausdorff’sche Dimensionen spezieller Punktmengen,

Math. Z. 76 (1961), 22-30.

[5] Ein gruppentheoretisches Analogon zum Begriff der normalen Zahl,

J. reine angew. Math. 206 (1961), 5-8.

[6] (gem. m. G. Helmberg) Neuere Entwicklungen der Theorie der Gleichverteilung,

Jahresber. DMV 64 (1961), 1-50.

[6a] Russische Übersetzung von [6], Mathematika 7,3 (1963), 3-46.

[7] (gem. m. B. Volkmann) Über die Häufigkeit von Zahlenfolgen mit gegebener Verteilungsfunktion,

Abh. Math. Seminar Hamburg 26 (1963), 39-54.

[8] Über eine Verallgemeinerung des Hauptsatzes der Theorie der Gleichverteilung,

J.reine angew. Math. 210 (1962), 141-147.

[9] Folgen normierter Maße auf kompakten Gruppen,

Z. Wahrscheinlichkeitstheorie 1 (1962), 3-13.

[10] Über die Grenzverteilung von Summen Markow’scher Ketten auf endlichen Gruppen I,

Z. Wahrscheinlichkeitstheorie 1 (1963), 415-420.

[11] Über die Grenzverteilung von Summen Markow’scher Ketten auf endlichen Gruppen II,

Z. Wahrscheinlichkeitstheorie 1 (1963), 421-432.

[12] (gem. m. L. Schmetterer) Über die Summe Markow’scher Ketten auf endlichen Gruppen,

Trans. 3. Prague Conf. on Information Theory, Prag 1964, 45-53.

[13] Einige Bemerkungen zur Theorie der fastperiodischen Funktionen,

Archiv Math. 15 (1964), 145-150.

[14] Methods of summability and uniform distribution mod 1,

Comp. Math. 16 (1964), 44-51.

[15] The fundamental theorem of van der Corput on uniform distribution and its generalizations,

Comp. Math. 16 (1964), 29-34.

[16] Some applications of the individual ergodic theorem to problems in number theory,

Comp. Math. 16 (1964), 35-43.

[17] Enige aspecten van de wiskundige begripsvorming,

J.B. Wolters, Groningen 1965, 16 S.

[18] Stark gleichverteilte Folgen in kompakten Gruppen,

Mh. Math. 70 (1966), 430-436.

[19] A characterization of well-distributed sequences,

Comp. Math. 17 (1967), 263-267.

[20] Invariant sigma - algebras on locally compact Abelian groups,

Indag. Math. 29 (1967), 375-377.

[21] Maßtreue, Rekurrenz und induzierte Transformationen,

Z. Wahrscheinlichkeitstheorie 11 (1968), 26-38.

[22] Some remarks on the distribution mod 1 of tempered sequences,

Nieuw Archief voor Wiskunde 16 (1968), 194-196.

[23] On a theorem of H. Weyl,

Comp. Math. 21 (1969), 151-154.

[24] Normed Ideals in L_1(G),

Indag. Math. 31 (1969), 273-282.

[25] Well-distributed sequences,

Bull. Soc. Math. France 25 (1971), 39-43.

[26] Funktoren auf Kategorien von Banachräumen,

Mh. Math. 78 (1974), 15-2.

[27] Tensor products of functors on categories of Banach spaces,

Lecture Notes in Math. 540 (1976), 164-185

[28] Zur Dualität von Funktoren, die durch Funktionenräume definiert sind,

Mh. Math. 82 (1976), 117-123.

[29] Some remarks on Rota’s umbral calculus,

Indag. Math. 40 (1978), 27-42.

[30] A note on a paper by L. Carlitz,

SIAM J. Math. Anal. 10 (1979), 78-79.

[31] Operatormethoden für q-Identitäten I,

Mh.Math. 88 (1979), 87-105.

[32] Operatormethoden für q-Identitäten II: q-Laguerre-Polynome,

Mh.Math. 91 (1981), 105-117.

[33] Operatormethoden für q-Identitäten III: Umbrale Inversion und die Lagrange’sche Formel,

Archiv Math. 35 (1980), 533-543.

[34] Elementare q-Identitäten,

Sem. Lotharingien Comb., Publ. IRMA 182/S-04, 1982, 261-267.

[35] Some remarks on Catalan Families,

Europ. J. Comb. 8 (1987), 261-267.

[36] Über die Anzahl erzeugender Mengen in endlichen Vektorräumen,

Anz. ÖAW 1992 Nr.5, 27-33.

[37] A new q-Analog of Stirling Numbers,

Sitzungsber. ÖAW 201 (1992), 97-109.

[38] Operatormethoden für q-Identitäten IV: Eine Klasse von q-Gould-Polynomen ,

Sitzungsber. ÖAW 205 (1996), 169-174.

[39] Operatormethoden für q-Identitäten V: q-Catalan-Bäume,

Sitzungsber. ÖAW 205 (1996), 175-182

[40] Operatormethoden für q-Identitäten VI: Geordnete Wurzelbäume und q-Catalan-Zahlen,

Sitzungsber. ÖAW 206 (1997), 253-266

[41] Mathematik zwischen Mythos und Konstruktion,

EuS 9 (1998), 432-435

[42] q-Catalan- und q-Motzkinzahlen,

Sitzungsber. ÖAW 208 (1999), 3-20

[43] Operatormethoden für q-Identitäten VII: q-Catalan-Determinanten,

Sitzungsber. ÖAW 208 (1999), 123-142

[44] Eine Charakterisierung der q-Exponentialpolynome,

Sitzungsber. ÖAW 208 (1999), 143-157

[45] Einige q-Analoga der Catalan-Zahlen,

Sitzungsber. ÖAW 209 (2000), 19-46

[46] q-Fibonacci polynomials,

Fibonacci Quarterly 41 (2003), 31-40

[47] Recurrences for some sequences of binomial sums,

Sitzungsber. ÖAW 210 (2001), 61-83

[48] Einige q-Analoga der Lucas- und Fibonacci-Polynome,

Sitzungsber. ÖAW 211 (2002), 3-20

[49] Some relations between generalized Fibonacci and Catalan numbers,

Sitzungsber. ÖAW 211 (2002), 143-154

[50] Some algebraic aspects of Morse code sequences,

Discrete Mathematics and Theoretical Computer Science 6 (2003), 055-068

[51] A new class of q-Fibonacci polynomials,

Electronic Journal of Combinatorics 10 (2003), R 19

[52] q-Fibonacci polynomials and the Rogers-Ramanujan identities,

Annals of Combinatorics 8 (2004), 269-285

[53] A class of Rogers-Ramanujan type recursions,

Sitzungsber. ÖAW 213 (2004), 71-93

[54] Fibonacci-Zahlen, Gitterpunktwege und die Identitäten von Rogers-Ramanujan,

Math. Semesterber. 52 (2005), 97-125

[55] Remarks on some sequences of binomial sums,

Sitzungsber. ÖAW 215 (2006), 139-153

[56] (gem. m. Christian Krattenthaler) Some determinants of path generating functions,

Adv. Appl. Math. 46 (2011), 144-174

[57] (gem. m. Jiang Zeng) A curious q-analogue of Hermite polynomials,

J. Comb. Th. A 118 (2011), 9-26

[58] (gem. m. Christian Krattenthaler) Hankel determinants of linear combinations of moments of orthogonal polynomials,

Int.J. Number Th. 17 (2021), 341-369

 

Preprints

 

q-Catalan numbers and q-Narayana polynomials

arXiv math CO/0507225

A note on some binomial sums,

arXiv math CO/0604431

Finite q-identities related to well-known theorems of Euler and Gauss,

arXiv math CO/0610546

Some results and conjectures about recurrence relations for certain sequences of binomial sums,

arXiv math CO/0611189

Simple proofs of Bressoud's and Schur's polynomial versions of the Rogers-Ramanujan identities,

arXiv math CO/0701802

q-Abel polynomials,

arXiv:0802.2886

Some conjectures about q-Fibonacci polynomials,

arXiv:0805.0415

Recurrence relations for powers of q-Fibonacci polynomials,

arXiv:0806.0805

Hankel determinants of Schroeder-like numbers,

arXiv:0901.4680

Hankel determinants of q-exponential polynomials,

arXiv:0901.4698

A simple approach to some Hankel determinants,

arXiv:0902.1650

q-Lucas polynomials and associated Rogers-Ramanujan type identities,

arXiv:0907.0165

q-Fibonacci polynomials and q-Genocchi numbers,

arXiv:0908.1219

Hankel determinants of generalized q-exponential polynomials,

arXiv:0909.5581

Some operator identities related to q-Hermite polynomials,

arXiv:1006.3210

Fibonacci polynomials, generalized Stirling numbers, and Bernoulli, Genocchi and tangent numbers,

arXiv:1103.2610

Some beautiful q-analogues of Fibonacci and Lucas polynomials,

arXiv:1104.2699

Some nice Hankel determinants,

arXiv:1109.1449

A simple approach to q-Chebyshev polynomials,

arXiv:1201.4703

q-Chebyshev polynomials,

arXiv:1205.5383

Ramanujan's q-continued fractions and Schroeder-like numbers,

arXiv:1210.0372

Hankel determinants of some polynomial sequences,

arXiv: 1211.0816

A special class of Hankel determinants,

arXiv:1302.4235

Recurrences for some sequences of binomial sums II: A simpler approach,

arXiv:1302.4239

Continuous q-Hermite polynomials: An elementary approach,

arXiv:1307.0357

Discrete q-Hermite polynomials: An elementary approach,

arXiv:1309.2082

Some remarks about q-Chebyshev polynomials and q-Catalan numbers and related results,

arXiv:1312.2767

Sum of cubes: Old proofs suggest new q-analogues,

arXiv:1403.6609

Some observations about super Catalan numbers, corresponding orthogonal polynomials, and their q-analogues,

arXiv:1410.0131

Some remarks and conjectures related to lattice paths in strips along the x-axis,

arXiv:1501.04750

Elementary observations on Rogers-Szegö polynomials,

arXiv:1602.07850

Some divisibility properties of q-Fibonacci numbers,

arXiv:1604.07977

Some elementary observations on Narayana polynomials and related topics,

arXiv:1611.05252

Some elementary observations on Narayana polynomials and related topics II: q-Narayana polynomials,

arXiv:1611.05256

Hankel determinants of harmonic numbers and related topics,

arXiv:1703.00763

Some remarks on Rogers-Szegö polynomials and Losanitsch's triangle,

arXiv:1711.03340

Catalan numbers, Hankel determinants and Fibonacci polynomials,

arXiv:1801.05608

A curious class of Hankel determinants,

arXiv:1803.05164

An interesting class of Hankel determinants, (with M. Tyson)

arXiv:1807.08330

Some observations about determinants which are connected with Catalan numbers and related topics,

arXiv:1902.10468

Some remarks on generalized Fibonacci and Lucas polynomials,

arXiv:1912.06651

Hankel determinants of linear combinations of moments of orthogonal polynomials, (with C. Krattenthaler

arXiv:2003.01676

Some remarks on the power product expansion of the q-exponential series,

arXiv:2006.06242

Bounded Dyck paths, bounded alternating sequences, orthogonal polynomials, and reciprocity, (with C. Krattenthaler)

arXiv:2012.03878

Pascal triangle, Hoggatt matrices, and analogous constructions,

arXiv:2103.01652

Shifted Hankel determinants of Catalan numbers and related results,

arXiv:2105.00660

Hankel determinants of middle binomial coefficients and conjectures for some polynomial extensions and modifications

arXiv:2111.14492

 

 

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