منابع مشابه
Enumerating split-pair arrangements
An arrangement of the multi-set {1,1,2,2, . . . , n, n} is said to be “split-pair” if for all i < n, between the two occurrences of i there is exactly one i + 1. We enumerate the number of split-pair arrangements and in particular show that the number of such arrangements is (−1)n+12n(22n − 1)B2n where Bi is the ith Bernoulli number. © 2007 Elsevier Inc. All rights reserved.
متن کاملEnumerating Row Arrangements of Three Species
This problem nicely illustrates the use of factorials and has a simple solution, though students often neglect the factor of two in the answer 2(N !)2. This omission can be instructive, as it leads naturally to generalizations of the problem: How does the answer change if there are N men and N − 1 women? What if men outnumber women by 2 or more? What if a sexist photographer insists that the li...
متن کاملEnumerating Permutations Avoiding A Pair Of Babson-Steingrimsson Patterns
Babson and Steingŕımsson introduced generalized permutation patterns that allow the requirement that two adjacent letters in a pattern must be adjacent in the permutation. Subsequently, Claesson presented a complete solution for the number of permutations avoiding any single pattern of type (1, 2) or (2, 1). For eight of these twelve patterns the answer is given by the Bell numbers. For the rem...
متن کاملEnumerating Permutations Avoiding a Pair of Babson-steingŕımsson Patterns
Babson and Steingŕımsson introduced generalized permutation patterns that allow the requirement that two adjacent letters in a pattern must be adjacent in the permutation. Subsequently, Claesson presented a complete solution for the number of permutations avoiding any single pattern of type (1, 2) or (2, 1). For eight of these twelve patterns the answer is given by the Bell numbers. For the rem...
متن کاملThe split decomposition of a tridiagonal pair
Let K denote a field and let V denote a vector space over K with finite positive dimension. We consider a pair of linear transformations A : V → V and A∗ : V → V that satisfy (i)–(iv) below: (i) Each of A, A∗ is diagonalizable. (ii) There exists an ordering V0, V1, . . . , Vd of the eigenspaces of A such that A ∗Vi ⊆ Vi−1 + Vi + Vi+1 for 0 ≤ i ≤ d, where V−1 = 0, Vd+1 = 0. (iii) There exists an...
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: 2008
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2007.06.003