Inequivalent factorizations of permutations
نویسندگان
چکیده
منابع مشابه
Inequivalent Transitive Factorizations into Transpositions
The question of counting minimal factorizations of permutations into transpositions that act transitively on a set has been studied extensively in the geometrical setting of ramified coverings of the sphere and in the algebraic setting of symmetric functions. It is natural, however, from a combinatorial point of view to ask how such results are affected by counting up to equivalence of factoriz...
متن کاملOn inequivalent factorizations of a cycle
We introduce a bijection between inequivalent minimal factorizations of the n-cycle (1 2 . . . n) into a product of smaller cycles of given length and trees of a certain structure. A factorization has the type α = (α2, α3, · · · ) if it has αj factors of length j. Inequivalent factorizations are defined up to reordering of commuting factors. A factorization is minimal if no factorizations of a ...
متن کاملFactorizations of Permutations Into Star Transpositions
We give a compact expression for the number of factorizations of any permutation into a minimal number of transpositions of the form (1 i). Our result generalizes earlier work of Pak in which substantial restrictions were placed on the permutation being factored.
متن کاملTransitive factorizations of permutations and geometry
We give an account of our work on transitive factorizations of permutations. The work has had impact upon other areas of mathematics such as the enumeration of graph embeddings, random matrices, branched covers, and the moduli spaces of curves. Aspects of these seemingly unrelated areas are seen to be related in a unifying view from the perspective of algebraic combinatorics. At several points ...
متن کاملMinimal Transitive Factorizations of Permutations into Cycles
We introduce a new approach to an enumerative problem closely linked with the geometry of branched coverings, that is, we study the number Hα(i2, i3, . . . ) of ways a given permutation (with cycles described by the partitionα) can be decomposed into a product of exactly i2 2-cycles, i3 3-cycles, etc., with certain minimality and transitivity conditions imposed on the factors. The method is to ...
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: 2016
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2015.12.002