Generalized Worpitzky Identities with Applications to Permutation Enumeration
نویسندگان
چکیده
منابع مشابه
Generalized Worpitzky Identities with Applications to Permutation Enumeration
The enumeration of permutations by inversions often leads to a q-analog of the usual generating 'nnetic,n. In this paper, two generalizations of the Worpitzky identity for the Eulerian numbers are obtained and used to enumerate permutations by the descent number and the major index of their inverses. The resulting (t, q)-generating series do in fact generalize the q-series obtainc? when countin...
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Let [n] stand for the first n natural numbers {1, 2, · · · , n} and Sn for the permutations of [n]. Given a permutation π = (a1, a2, · · · , an) ∈ Sn, a rise (shortly as “R”) at the kth position refers to ak < ak+1, while a fall (shortly as “F”) at the same position refers to ak > ak+1, where the position index k runs from 1 to n − 1. It is classically well–known (cf. Comtet [2, §6.5]) that the...
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We develop algorithmic tools to compute quickly the distribution of permutation statistics over sets of pattern-avoiding permutations. More specfically, the algorithms are based on enumeration schemes, the permutation statistics are based on the number of occurrences of certain vincular patterns, and the permutations avoid sets of vincular patterns. We prove that whenever a finite enumeration s...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 1981
ISSN: 0195-6698
DOI: 10.1016/s0195-6698(81)80023-6