The (q, r)-Eulerian polynomials are the (maj−exc, fix, exc) enumerative polynomials of permutations. Using Shareshian and Wachs’ exponential generating function of these Eulerian polynomials, Chung and Graham proved two symmetrical q-Eulerian identities and asked for bijective proofs. We provide such proofs using Foata and Han’s three-variable statistic (inv−lec, pix, lec). We also prove a new ...

195 1Center of General Education, Chung-Yuan Christian University, Chung-Li, Taiwan 2Atmospheric Sciences Research Center, State University of New York, at Albany, New York, USA *Corresponding author address: Prof. Ho-Ching Lee, Center of General Education, Chung-Yuan Christian University, Chung-Li, Taiwan, ROC; E-mail: [email protected] Aviation emissions of trace gases (NO x , CO, H 2 O, an...

Haviland and Thomason and Chung and Graham were the first to investigate systematically some properties of quasi-random hypergraphs. In particular, in a series of articles, Chung and Graham considered several quite disparate properties of random-like hypergraphs of density 1/2 and proved that they are in fact equivalent. The central concept in their work turned out to be the so called deviation...

Supervisory control of discrete event systems using limited lookahead has been studied by Chung-Lafortune-Lin, where control is computed by truncating the plant behavior up to the limited lookahead window. We present a modification of this approach in which the control is computed by extending the plant behavior by arbitrary traces beyond the limited lookahead window. The proposed supervisor av...