[seqfan] Does FindStat ST000155 match with A008292?

Susanne Wienand susanne.wienand at gmail.com
Mon Aug 18 23:21:18 CEST 2014


Dear Seqfans,

the generating functions which are listed at ST000155 of FindStat
<http://www.findstat.org/StatisticsDatabase/St000155/> seem to match with
A008292 <http://oeis.org/A008292>, Eulerian numbers.
According to Xiong, Hall and Tsao <http://dx.doi.org/10.1155/2014/870596>,
the Eulerian numbers A(n,k) count permutations of length n with k *weak*
exceedances (p(i) >= i).
However, ST000155 lists numbers of exceedances (p(i) > i) of permutations.
It seems that A(n,k) also counts permutations of length n with k-1
exceedances.
Are both, permutations with weak exceedances and permutations with
exceedances, counted by the Eulerian numbers?

Regards
Susanne



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