Journal of Integer Sequences, Vol. 5 (2002), Article 02.1.5

Young tableaux and other mutually describing sequences

Zoran Sunik

Department of Mathematics and Statistics
810 Oldfather Hall
University of Nebraska
Lincoln, NE 68588-0323
USA

Abstract: We introduce a transformation on integer sequences for which the set of images is in bijective correspondence with the set of Young tableaux. We use this correspondence to show that the set of images, known as ballot sequences, is also the set of double points of our transformation. In the second part, we introduce other transformations of integer sequences and show that, starting from any sequence, repeated applications of the transformations eventually produce a fixed point (a self-describing sequence) or a double point (a pair of mutually describing sequences).

(Concerned with sequence A071962 .)

Received March 19, 2002; revised version received June 28, 2002. Published in Journal of Integer Sequences August 30, 2002.