منابع مشابه
Shuffle-compatible permutation statistics II: the exterior peak set
5. Dendriform structures 59 5.1. Four operations on QSym . . . . . . . . . . . . . . . . . . . . . . . . 59 5.2. Ideals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 5.3. Application to KEpk . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 5.4. Dendriform shuffle-compatibility . . . . . . . . . . . . . . . . . . . . 67 5.5. Criteria for Kst to be a stack i...
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During compilation of a program, register allocation is the task of mapping program variables to machine registers. During register allocation, the compiler may introduce shuffle code, consisting of copy and swap operations, that transfers data between the registers. Three common sources of shuffle code are conflicting register mappings at joins in the control flow of the program, e.g, due to i...
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The shuffle-exchange permutation network (SEPn) is a fixed degree Cayley graph which has been proposed as a basis for massively parallel systems. We propose a routing algorithm with an upper bound of (5/8)n + O(n), where n is the length of the permutation. (This improves on a (9/8)n routing algorithm described earlier [5].) Thus, the diameter of SEPn is at most (5/8) n 2 + O(n). We also show th...
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This article is devoted to the study of monoids which can be endowed with a shuffle product with coefficients in a semiring. We show that, when the multiplicities do not belong to a ring with prime characteristic, such a monoid is a monoid of traces. When the characteristic is prime, we give a decomposition of the congruences ≡ (or relators R) such that A∗/≡ = 〈A;R〉 admits a shuffle product. Th...
متن کاملPermutation patterns and statistics
Call two sequences of distinct integers a1a2 . . . ak and b1b2 . . . bk order isomorphic if they have the same pairwise comparisons, i.e., ai < aj if and only if bi < bj for all indices i, j. For example 132 and 475 are order isomorphic since both begin with the smallest element, have the largest element second, and end with the middle sized element. Let Sn be the set of all permutations of {1,...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2018
ISSN: 0001-8708
DOI: 10.1016/j.aim.2018.05.003