We explicitly evaluate the generating functions for joint distributions of pairs of the permutation statistics inv, maj and ch over the symmetric group when both variables are set to −1. We give a combinatorial proof by means of a sign-reversing involution that specializing the variables to −1 in these bimahonian generating functions gives the number of two-colored permutations up to sign.

We find an explicit closed form for the subword complexity of the infinite fixed point of the morphism sending a → aab and b → b. This morphism is then generalized in three different ways, and we find similar explicit expressions for the subword complexity of the generalizations.

In light of these trends, this article offers an in-depth exploration of racial and ethnic achievement gap trends and a preliminary examination of different factors that may interact to influence the trends. It offers a comprehensive review of available data on the Black-White and Hispanic-White achievement gaps in reading and mathematics over the last three decades. The achievement gap is meas...

This paper presents a subword normalized cut (N-cut) approach to automatic story segmentation of Chinese broadcast news (BN). We represent a speech recognition transcript using a weighted undirected graph, where the nodes correspond to sentences and the weights of edges describe inter-sentence similarities. Story segmentation is formalized as a graph-partitioning problem under the N-cut criteri...

This paper focuses on the following two points: First, we try to clarify the effect of combination systems from two aspects, accuracy and heterogeneity. And then we evaluate our unique subword unit, called Sub-Phonetic Segment (SPS) to maximize performance improvement by combination. Combination systems usually yield higher performance than any individual system. When the systems being combined...

We derive a lower bound for the subword complexity of the base-b expansion (b ≥ 2) of all real numbers whose irrationality exponent is equal to 2. This provides a generalization of a theorem due to Ferenczi and Mauduit. As a consequence, we obtain the first lower bound for the subword complexity of the number e and of some other transcendental exponential periods.