×

zbMATH — the first resource for mathematics

Pascal triangles, Catalan numbers and renewal arrays. (English) Zbl 0398.05007

MSC:
05A15 Exact enumeration problems, generating functions
05A19 Combinatorial identities, bijective combinatorics
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Carlitz, L., Solution of certain recurrences, SIAM J. appl. math., 17, 251-269, (1969) · Zbl 0177.02101
[2] Carlitz, L., Note on the numbers of Jordan and Ward, Duke. math. J., 38, 783-790, (1971) · Zbl 0228.05005
[3] Donaghey, R.; Shapiro, L.W., Motzkin numbers, J. combinatorial. theory ser. A, 28, 291-301, (1977) · Zbl 0417.05007
[4] Fine, T., Extrapolation when very little is known, Information and control, 16, 331-360, (1970) · Zbl 0205.44003
[5] Forder, H.G., Some problems in combinatorics, Math. gaz., 45, 199-201, (1961) · Zbl 0098.24503
[6] Gardner, M., Mathematical games, Sci. am., 234, 6, 120-125, (1976)
[7] Gould, H.W., Final analysis of Vandermonde’s convolution, Am. nath. monthly, 64, 409-415, (1957) · Zbl 0079.01005
[8] Gould, H.W.; Gould, H.W., Research bibliography of two special number sequences, (), revised · Zbl 0226.10002
[9] Krigman, J.F.C., Regenerative phenomena, (1972), Wiley London · Zbl 0236.60040
[10] Klarner, D.A., Correspondence between plane trees and binary sequences, J. combinatorial theory, 9, 401-411, (1970) · Zbl 0205.54702
[11] Riordan, J., Introduction to combinatorial analysis, (1958), Wiley New York · Zbl 0078.00805
[12] D.G. Rogers, An application of renewal sequences to the dinner problem.
[13] Rogers, D.G., Similarity relations on totally ordered sets, J. combinatorial. theory ser. A, 23, 88-98, (1977) · Zbl 0366.06001
[14] Rogers, D.G., The enumeration of a family of ladder graphs by edges. part I: connective relations, Quart. J. math. Oxford, 28, 2, (1977) · Zbl 0373.05045
[15] Rogers, D.G., A Schröder triangle: three combinatorial problems, (), Lecture Notes in Mathematics · Zbl 0368.05004
[16] D.G. Rogers, A note on the enumeration of lattice paths with diagonal steps.
[17] Shapiroc, L.W., A Catalan triangle, Discrete math., 14, 83-90, (1976) · Zbl 0323.05004
[18] Sloane, N.J.A., A handbook of integer sequences, (1973), Academic Press New York · Zbl 0286.10001
[19] Speed, T.P., Geometric and probabilistic aspects of some combinatorial identities, J. aust. math. soc., 22, A, 462-468, (1976) · Zbl 0348.05008
[20] Sved, M., Generalized binomial coefficients, (), Lecture Notes in Mathematics
[21] van Lint, J.H., Combinatorial theory seminar, Eindhoven university of technology, () · Zbl 0315.05001
[22] Wendel, J.G., Left-continuous random walk and the Lagrange expansion, Am. math. monthly, 82, 494-499, (1975) · Zbl 0304.60040
[23] Whittaker, E.T.; Watson, G.N., A course of modern analysis, (1946), Cambridge Univ. Press London · Zbl 0108.26903
[24] Yaglom, A.M.; Yaglom, I.M., Challenging problems in mathematics with elementary solutions, Vol. 1, (1964), Holden Day San Francisco · Zbl 0123.24201
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.