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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.
We present analytical properties of a sequence of integers related to the evaluation of a rational integral. We also discuss an algorithm for the evaluation of the 2-adic valuation of these integers that has a combinatorial interpretation.
It is proposed that finding the recursion relation and generating function for the (colored) Motzkin numbers of higher rank introduced recently is an interesting problem.
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