Decreases and Descents in Words
نویسندگان
چکیده
The generating function for words by a multivariable statistic involving decrease, increase, descent and rise values is explicitly calculated by using the MacMahon Master Theorem and the properties of the first fundamental transformation on words. Applications to statistical study of the symmetric group are also given.
منابع مشابه
Descent distribution on Catalan words avoiding a pattern of length at most three
Catalan words are particular growth-restricted words over the set of non-negative integers, and they represent still another combinatorial class counted by the Catalan numbers. We study the distribution of descents on the sets of Catalan words avoiding a pattern of length at most three: for each such a pattern p we provide a bivariate generating function where the coefficient of xy in its serie...
متن کاملCounting ordered patterns in words generated by morphisms I. Rises, descents, and repetitions with gaps
We start a general study of counting the number of occurrences of ordered patterns in words generated by morphisms. The case of rises and descents is considered. We give recurrence formulas in the general case. We deduce exact formulas for a particular family of morphisms.
متن کاملA Combinatorial and Probabilistic Study of Initial and End Heights of Descents in Samples of Geometrically Distributed Random Variables and in Permutations
LetX be a random variable (RV), distributed according to the geometric distribution with parameter p (geom(p)): P(X = k) = pq, with q = 1 − p. We consider a sequence X1X2 . . . Xn of independent RVs. We also speak about words a1 . . . an; there is some interest of combinatorial parameters of such words, generated by independent geometric random variables. In this paper we continue the study of ...
متن کاملIntervals of permutations with a fixed number of descents are shellable
The set of all permutations, ordered by pattern containment, is a poset. We present an order isomorphism from the poset of permutations with a fixed number of descents to a certain poset of words with subword order. We use this bijection to show that intervals of permutations with a fixed number of descents are shellable, and we present a formula for the Möbius function of these intervals. We p...
متن کاملCounting Descents, Rises, and Levels, with Prescribed First Element, in Words
Recently, Kitaev and Remmel [8] refined the well-known permutation statistic “descent” by fixing parity of one of the descent’s numbers. Results in [8] were extended and generalized in several ways in [7, 9, 10, 11]. In this paper, we shall fix a set partition of the natural numbers N, (N1, . . . ,Nt), and we study the distribution of descents, levels, and rises according to whether the first l...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007