TY - JOUR
T1 - Counting descents, rises, and levels, with prescribed first element, in words
AU - Kitaev, Sergey
AU - Mansour, Toufik
AU - Remmel, Jeffrey
PY - 2008
Y1 - 2008
N2 - Recently, Kitaev and Remmel [9] re¯ned the well-known permutation statistic \descent" by ¯xing parity of one of the descent's numbers. Results in [9] were extended and generalized in several ways in [7, 10, 11, 12]. In this paper, we shall ¯x a set partition of the natural numbers N, (N1; : : : ;Ns), and we study the distribution of descents, levels, and rises according to whether the ¯rst letter of the descent, rise, or level lies in Ni over the set of words over the alphabet [k] = f1; : : : ; kg. In particular, we re¯ne and generalize some of the results in [4].
AB - Recently, Kitaev and Remmel [9] re¯ned the well-known permutation statistic \descent" by ¯xing parity of one of the descent's numbers. Results in [9] were extended and generalized in several ways in [7, 10, 11, 12]. In this paper, we shall ¯x a set partition of the natural numbers N, (N1; : : : ;Ns), and we study the distribution of descents, levels, and rises according to whether the ¯rst letter of the descent, rise, or level lies in Ni over the set of words over the alphabet [k] = f1; : : : ; kg. In particular, we re¯ne and generalize some of the results in [4].
KW - distribution of descents
KW - rises
KW - levels
KW - permutation statistics
UR - http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/680
UR - https://personal.cis.strath.ac.uk/sergey.kitaev/index_files/Papers/deslevris-words.pdf
M3 - Article
SN - 1365-8050
VL - 10
JO - Discrete Mathematics and Theoretical Computer Science
JF - Discrete Mathematics and Theoretical Computer Science
IS - 3
ER -