Related papers: RSK-Complete Cycle Decompositions

Let $ (\rho, V) $ be an irreducible representation of the symmetric group $ S_n$ (or the alternating group $ A_n$), and let $ g $ be a permutation on $n$ letters with each of its cycle lengths divides the length of its largest cycle. We…

We study the shape of the Young diagram \lambda associated via the Robinson-Schensted-Knuth algorithm to a random permutation in S_n such that the length of the longest decreasing subsequence is not bigger than a fixed number d; in other…

In [F. Caselli, Involutory reflection groups and their models, J. Algebra 24 (2010), 370--393] it is constructed a uniform Gelfand model for all non-exceptional irreducible complex reflection groups which are involutory. This model can be…

We prove a number of results, new and old, about the cycle type of a random permutation on S_n. Underlying our analysis is the idea that the number of cycles of size k is roughly Poisson distributed with parameter 1/k. In particular, we…

We consider facet-Hamiltonian cycles of polytopes, defined as cycles in their skeleton such that every facet is visited exactly once. These cycles can be understood as optimal watchman routes that guard the facets of a polytope. We consider…

We construct the analogue of the plactic monoid for the super semistandard Young tableaux over a signed alphabet. This is done by developing a generalization of the Knuth's relations. Moreover we get generalizations of Greene's invariants…

We investigate the dynamics of the well-known RSK bijection on permutations when iterated on various reading words of the recording tableau. In the setting of the ordinary (row) reading word, we show that there is exactly one fixed point…

In symmetric groups, a two-sided cell is the set of all permutations which are mapped by the Robinson-Schensted correspondence on a pair of tableaux of the same shape. In this article, we show that the set of permutations in a two-sided…

Let $m, n$ be positive integers such that $m>1$ divides $n$. In this paper, we introduce a special class of piecewise-affine permutations of the finite set $[1, n]:=\{1, \ldots, n\}$ with the property that the reduction $\pmod m$ of $m$…

A universal cycle for a set S of combinatorial objects is a cyclic sequence of length |S|that contains a representation of each element in S exactly once as a substring. If S is the set of k-subsets of [n] = {1, 2, . . . , n}, it is…

For each fully commutative permutation, we construct a "boolean core," which is the maximal boolean permutation in its principal order ideal under the right weak order. We partition the set of fully commutative permutations into the…

We continue the classification of 2-dimensional scale-invariant rigid special Kahler (RSK) geometries. This classification was begun in [hep-th/0504070] where singularities corresponding to curves of the form y^2=x^6 with a fixed canonical…

The problem of finding Schur-positive sets of permutations, originally posed by Gessel and Reutenauer, has seen some recent developments. Schur-positive sets of pattern-avoiding permutations have been found by Sagan et al and a general…

The cycle-preserving symmetries for the nine two-dimensional real spaces of constant curvature are collectively obtained within a Cayley-Klein framework. This approach affords a unified and global study of the conformal structure of the…

The number of standard Young tableaux of a fixed shape is famously given by the hook-length formula due to Frame, Robinson and Thrall. A bijective proof of Novelli, Pak and Stoyanovskii relies on a sorting algorithm akin to jeu-de-taquin…

P-resolutions of a cyclic quotient singularity are known to be in one-to-one correspondence with the components of the base space of its semi-universal deformation. Stevens and Christophersen have shown that P-resolutions are parametrized…

The work of Vershik and Kerov [1977], Logan and Shepp [1977] established that the shape of the scaled random young diagram in Russian notation, as determined by the Plancherel measure, converges to a deterministic shape. In this article, we…

The problem whether a given permutation group contains a permutation with a given cycle type is studied. This problem is known to be NP-complete. In this paper it is shown that the problem can be solved in logspace for a cyclic permutation…

We study isolated quotient singularities by finite and linearly reductive group schemes (lrq singularities for short) and show that they satisfy many, but not all, of the known properties of finite quotient singularities in characteristic…

Let the sign of a skew standard Young tableau be the sign of the permutation you get by reading it row by row from left to right, like a book. We examine how the sign property is transferred by the skew Robinson-Schensted correspondence…