Tran-Ngoc Danh, David E. Daykin
Bezrukov-Gronau Order is Not Optimal
The paper is published: Rostocker Mathematisches Kolloquium, Rostock. Math. Kolloq. 50, 45-46 (1997)

MSC:

05A99 None of the above but in this section

06A07 Combinatorics of partially ordered sets

Abstract: Let $N$ be the integers $\geq 0$. For $n\in N$ let $V(n)$ be the vectors
$\underset{\displaystyle\tilde{}}{a}=(a_1,\ldots ,a_n)$ with $a_i\in N$,
and
$C(n)$ be
the vectors with $a_i\in\{0,1\}$. For $1\leq i\leq n$ let
$\delta_i\underset{\displaystyle\tilde{}}{a}\in V(n-1)$ be obtained from
$\underset{\displaystyle\tilde{}}{a}$ by deleting
$a_i$.
The shadow $ \Delta\underset{\displaystyle\tilde{}}{a}$ is
$\{\delta_1\underset{\displaystyle\tilde{}}{a},\ldots
,\delta_n\underset{\displaystyle\tilde{}}{a}\}\subseteq V(n-1)$. For
$A\subseteq V(n)$ we
put $\Delta
A=\bigcup\{\underset{\displaystyle\tilde{}}{a}\in
A\}\Delta\underset{\displaystyle\tilde{}}{a}$.
Keywords: Combinatorial problems; Combinatorics of partially ordered sets; Combinatorics on words