My half-century journey started from synthetic organic chemistry. During the first stage of my journey, my interest in stereochemistry was initiated through the investigation on the participation of steric effects in reactive intermediates, cylophanes, strained heterocycles, and organic compounds for photography. In chemoinformatics as the next stage of the journey, I proposed the concept of im...

We describe a provably complete algorithm for the generation of a tight, possibly exact, superset of all combinatorially distinct simple n-facet polytopes in Rd, along with their graphs, f -vectors, and face lattices. The technique applies repeated cutting planes and planar sweeps to a d−simplex. Our generator has implications for several outstanding problems in polytope theory, including conje...

An original combinatorial proof of a combinatorial identity is presented. Key words, combinatorial enumeration, graph theory AMS(MOS) subject classification. 05A19

It is well known that the set of $m$-Dyck paths with a fixed height and amount valleys counted by Fu{\ss}-Narayana numbers. In this article, we consider start at least $t$ north steps. We give exact formulas for number such height, returns (i) valleys, (ii) $x$-coordinate divisible $m$ (iii) not $m$. The enumeration combinatorially realizes $H$-triangle appearing in recent article Krattenthaler...