New combinatorial interpretations of some mock theta functions
نویسنده
چکیده
In 1972, Bender and Knuth established a bijection between certain infinite matrices of non-negative integers and plane partitions and in [2] a bijection between Bender-Knuth matrices and n-color partitions was shown. Here we use this later bijection and translate the recently found n-color partition theoretic interpretations of four mock theta functions of S. Ramanujan in [1] to new combinatorial interpretations of the same mock theta functions involving Bender-Knuth matrices. Subject Class: 05A15, 05A17, 11P81
منابع مشابه
A new approach and generalizations to some results about mock theta functions
Some Mock Theta functions have been interpreted in terms of n-color partition. In this paper we use a new technique to gain a deeper insight on these interpretations, as well as we employ this new technique to obtain in a more systematic way similar new interpretations for three other mock theta functions. keywords: mock theta functions, n-color partitions, combinatorial interpretations, modula...
متن کاملSplit $(n+t)$-Color Partitions and Gordon-McIntosh Eight Order Mock Theta Functions
In 2004, the first author gave the combinatorial interpretations of four mock theta functions of Srinivasa Ramanujan using n-color partitions which were introduced by himself and G.E. Andrews in 1987. In this paper we introduce a new class of partitions and call them “split (n+t)-color partitions”. These new partitions generalize Agarwal–Andrews (n + t)-color partitions. We use these new combin...
متن کاملOn combinatorial extensions of some mock theta functions using signed partitions
Recently Agarwal and Sood, in their paper entitled “Split (n+ t)−color partitions and Gordon-McIntosh eight order mock theta functions, The Electronic Journal of Combinatorics 21(2), (2014), #P2.46”, have defined and used the ‘split (n+t)−color partitions’ to obtain the combinatorial interpretations of two mock theta functions. The purpose of this paper is to extend their results using ‘signed ...
متن کاملn-Color Partition Theoretic Interpretations of some Mock Theta Functions
Using n-color partitions we provide new number theoretic interpretations of four mock theta functions of S. Ramanujan.
متن کاملOn flushed partitions and concave compositions
Abstract. In this work, we give combinatorial proofs for generating functions of two problems, i.e. flushed partitions and concave compositions of even length. We also give combinatorial interpretation of one problem posed by Sylvester involving flushed partitions and then prove it. For these purposes, we first describe an involution and use it to prove core identities. Using this involution wi...
متن کامل