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10.921  Articles
1 of 1.093 pages  |  10  records  |  more records»
This paper is a continuation of the work "Shuffle-compatible permutation statistics" by Gessel and Zhuang (but can be read independently from the latter). We study the shuffle-compatibility of permutation statistics — a concept introduced by Gessel and Zh... see more

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... see more

We show that the bistatistic of right nestings and right crossings in matchings without left nestings is equidistributed with the number of occurrences of two certain patterns in permutations, and furthermore that this equidistribution holds when refined ... see more

We study relationships between permutation statistics and pattern-functions, counting the number of times particular patterns occur in a permutation. This allows us to write several familiar statistics as linear combinations of pattern counts, both in ter... see more

In this paper, we study the relationship among left peaks, interior peaks and up-down runs of simsun permutations. Properties of the generating polynomials, including the recurrence relation, generating function and real-rootedness are studied. Moreover, ... see more

We study relationships between permutation statistics and pattern-functions, counting the number of times particular patterns occur in a permutation. This allows us to write several familiar statistics as linear combinations of pattern counts, both in ter... see more

We present a bijection between permutation matrices and descending plane partitions without special parts, which respects two of the statistics considered by Mills, Robbins and Rumsey, and an additional statistic  considered by Behrend, Di ... see more

We prove various formulas which express exponential generating functions counting permutations by the peak number, valley number, double ascent number, and double descent number statistics in terms of the exponential generating function for Chebyshev poly... see more

We prove various formulas which express exponential generating functions counting permutations by the peak number, valley number, double ascent number, and double descent number statistics in terms of the exponential generating function for Chebyshev poly... see more

1 of 1.093 pages  |  10  records  |  more records»