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Partition Identities for Ramanujan's Third Order Mock Theta Functions
mock theta function Ramanujan's identities partition identity Fine's theorem involution
2014/6/3
We find two involutions on partitions that lead to partition identities for Ramanujan's third order mock theta functions φ(-q) and ψ(-q). We also give an involution for Fine's partition identity on th...
Generalized determinantal identities involving Lucas polynomials
Fibonacci number Lucas number Fibonacci polynomial
2010/9/10
Determinants have played a significant part in various areas in mathematics. There are different perspectives on the study of determinants. Many problems on determinants of Fibonacci sequence and Luca...
Rational Identities and Inequalities involving Fibonacci and Lucas Numbers
Rational Identities and Inequalities Sequences of Integers Fibonacci and Lucas numbers
2008/6/27
In this paper we use integral calculus, complex variable techniques and some classical inequalities to establish rational identities and inequalities involving Fibonacci and Lucas numbers.
Rational Identities and Inequalities
Rational Identities and Inequalities Fibonacci numbers Lucas numbers Pell numbers
2008/6/27
Recently, in [4] the author studied some rational identities and inequalities involving Fibonacci and Lucas numbers. In this paper we generalize these rational identities and inequalities to involve a...
Identities from Weighted Motzkin Paths
Narayana number Catalan number Motzkin path Weighted Motzkin path Multiple Dyck path Bijection
2014/6/3
Based on a weighted version of the bijection between Dyck paths and 2-Motzkin paths, we find combinatorial interpretations of two identities related to the Narayana polynomials and the Catalan numbers...
Matrix Identities on Weighted Partial Motzkin Paths
Catalan number Schroder number Dyck path Motzkin path partial Motzkin path free Motzkin path weighted Motzkin path Riordan array
2014/6/3
We give a combinatorial interpretation of a matrix identity on Catalan numbers and the sequence (1, 4, 42, 43, ...) which has been derived by Shapiro, Woan and Getu by using Riordan arrays. By giving ...