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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Singleton mesh patterns in multidimensional permutations
多维排列 Singleton网格模式 排列模式
2023/11/13
Permutation patterns is a popular area of research introduced in 1968, but with roots going to the work of Leonhard Euler in 1749.
STRUCTURE OF THE MALVENUTO-REUTENAUER HOPF ALGEBRA OF PERMUTATIONS
Hopf algebra symmetric group weak order quasi-symmetric function
2015/8/14
We analyze the structure of theMalvenuto-Reutenauer Hopf algebraSSym
of permutations in detail. We give explicit formulas for its antipode, prove that it is
a cofree coalgebra, determine its primiti...
COCOMMUTATIVE HOPF ALGEBRAS OF PERMUTATIONS AND TREES
Hopf algebr rooted tree planar binary tree symmetric group
2015/8/14
Consider the coradical filtrations of the Hopf algebras of planar binary
trees of Loday and Ronco and of permutations of Malvenuto and Reutenauer. We
give explicit isomorphisms showing that the asso...
THE HOPF ALGEBRA OF UNIFORM BLOCK PERMUTATIONS
Hopf algebra factorizable inverse monoid uniform block permutation
2015/8/14
We introduce the Hopf algebra of uniform block permutations and show that
it is self-dual, free, and cofree. These results are closely related to the fact that uniform
block permutations form a fact...
STATISTICAL PROBLEMS INVOLVING PERMUTATIONS WITH RESTRICTED POSITIONS
Application the displacement test independent truncated data extrasensory perception
2015/7/14
The rich world of permutation tests can be supplemented by a variety of applications where only some permutations are permitted. We consider two examples testing independence with truncated data and ...
UNSEPARATED PAIRS AND FIXED POINTS IN RANDOM PERMUTATIONS
Unseparated pairs fixed points random arrangement
2015/7/7
UNSEPARATED PAIRS AND FIXED POINTS IN RANDOM PERMUTATIONS。
On Pattern Avoiding Alternating Permutations
alternating permutation pattern avoidance generating tree
2014/6/3
An alternating permutation of length n is a permutation π = π1π2...πn such that π1 < π2 > π3 < π4 >.... Let An denote the set of alternating permutations of {1, 2,..., n}, and let An(σ) be the set of ...
Cycles and sorting index for matchings and restricted permutations
Cycles and sorting index matchings and restricted permutations Combinatorics
2012/6/25
We prove that the Mahonian-Stirling pairs of permutation statistics $(\sor, \cyc)$ and $(\inv, \mathrm{rlmin})$ are equidistributed on the set of permutations that correspond to arrangements of $n$ no...
Permutations all of whose patterns of a given length are distinct
Permutations a given length distinct Combinatorics
2012/6/21
For each integer k >= 2, let F(k) denote the largest n for which there exists a permutation \sigma \in S_n, all of whose patterns of length k are distinct. We prove that F(k) = k + \lfloor \sqrt{2k-3}...
Partially 2-Colored Permutations and the Boros-Moll Polynomials
partially 2-colored permutation Boros-Moll polynomial rising factorial logconcavity bijection
2014/6/3
We find a combinatorial setting for the coefficients of the Boros-Moll polynomials Pm(a) in terms of partially 2-colored permutations. Using this model, we give a combinatorial proof of a recurrence r...
Separation probabilities for products of permutations
Separation probabilities products permutations fixed cycle types
2012/3/1
We study the mixing properties of permutations obtained as a product of two uniformly random permutations of fixed cycle types. For instance, we give an exact formula for the probability that elements...
Minimal Permutations and 2-Regular Skew Tableaux
minimal permutation 2-regular skew tableau Knuth equivalence the RSK algorithm
2014/6/3
Bouvel and Pergola introduced the notion of minimal permutations in the study of the whole genome duplication-random loss model for genome rearrangements. Let Fd(n) denote the set of minimal permutati...
The problem of genealogy of permutations has been solved par-tially by Stefan (odd order) and Acosta-Humanez & Bernhardt (power of two).It is well known that Sharkovskii's theorem shows the relations...
Matrices with restricted entries and q-analogues of permutations
Matrices q-analogues of permutations
2010/11/23
We study the functions that count matrices of given rank over a finite field with specified positions equal to zero. We show that these matrices are $q$-analogues of permutations with certain restrict...
Algebraic and combinatorial structures on Baxter permutations
Algebraic combinatorial structures Baxter permutations
2010/11/23
We construct a Hopf subalgebra of the Hopf algebra of Free quasi-symmetric functions whose bases are indexed by objects belonging to the Baxter combinatorial family (i.e. Baxter permutation, pairs of ...