Symmetric multisets of permutations
نویسندگان
چکیده
منابع مشابه
Stirling permutations on multisets
A permutation σ of a multiset is called Stirling permutation if σ(s) ≥ σ(i) as soon as σ(i) = σ(j) and i < s < j. In our paper we study Stirling polynomials that arise in the generating function for descent statistics on Stirling permutations of any multiset. We develop generalizations of the classical Stirling numbers and present their combinatorial interpretations. Particularly, we apply the ...
متن کاملSymmetric and Asymptotically Symmetric Permutations
We consider two related problems arising from a question of R. Graham on quasirandom phenomena in permutation patterns. A “pattern” in a permutation σ is the order type of the restriction of σ : [n] → [n] to a subset S ⊂ [n]. First, is it possible for the pattern counts in a permutation to be exactly equal to their expected values under a uniform distribution? Attempts to address this question ...
متن کاملNormal Approximations for Descents and Inversions of Permutations of Multisets
Normal approximations for descents and inversions of permutations of the set {1, 2, . . . , n} are well known. We consider the number of inversions of a permutation π(1), π(2), . . . , π(n) of a multiset with n elements, which is the number of pairs (i, j) with 1 ≤ i < j ≤ n and π(i) > π(j). The number of descents is the number of i in the range 1 ≤ i < n such that π(i) > π(i + 1). We prove tha...
متن کاملPermutations of the Natural Numbers with Prescribed Difference Multisets
We study permutations π of the natural numbers for which the numbers π(n) are chosen greedily under the restriction that the differences π(n)−n belong to a given (multi)subset M of Z for all n ∈ S, a given subset of N. Various combinatorial properties of such permutations (for quite general M and S) are exhibited and others conjectured. Our results generalise to a large extent known facts in th...
متن کاملSpherically Symmetric Random Permutations
We consider random permutations which are spherically symmetric with respect to a metric on the symmetric group Sn and are consistent as n varies. The extreme infinitely spherically symmetric permutation-valued processes are identified for the Hamming, Kendall-tau and Caley metrics. The proofs in all three cases are based on a unified approach through stochastic monotonicity. MSC:
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2020
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2020.105255