Related papers: Standard Rothe Tableaux
We define a map between the set of permutations that avoid either the four patterns $3214,3241,4213,4231$ or $3124,3142,4123,4132$, and the set of Dyck prefixes. This map, when restricted to either of the two classes, turns out to be a…
A fundamental identity in the representation theory of the partition algebra is $n^k = \sum_{\lambda} f^\lambda m_k^\lambda$ for $n \geq 2k$, where $\lambda$ ranges over integer partitions of $n$, $f^\lambda$ is the number of standard Young…
We give a positive equivariant Littlewood-Richardson rule also discovered independently by Molev. Our proof generalizes a proof by Stembridge of the ordinary Littlewood-Richardson rule. We describe a weight-preserving bijection between our…
Following Cand\`es, Romberg and Tao (IEEE Transactions on Information Theory 20,2 (2006) 489-509) a signal is represented as a function x defined on the cyclic group G = Z / NZ, and assuming that it is carried by a set S consisting of T…
We study the graph on reduced words with edges given by the Coxeter relations for the symmetric group. We define a metric on reduced words for a given permutation, analogous to Coxeter length for permutations, for which the graph becomes…
Our main result is a limit shape theorem for the two-dimensional surface defined by a uniform random n-by-n square Young tableau. The analysis leads to a calculus of variations minimization problem that resembles the minimization problems…
We study an iterative matrix conditioning algorithm due to Osborne (1960). The goal of the algorithm is to convert a square matrix into a balanced matrix where every row and corresponding column have the same norm. The original algorithm…
For their bijective proof of the hook-length formula for the number of standard tableaux of a fixed shape Novelli, Pak and Stoyanovskii define a modified jeu de taquin which transforms an arbitrary filling of the Ferrers diagram with…
In this manuscript we show that two partial orders defined on the set of standard Young tableaux of shape $\alpha$ are equivalent. In fact, we give two proofs for the equivalence of the box order and the dominance order for {tableaux}. Both…
An involution in a Coxeter group has an associated set of involution words, a variation on reduced words. These words are saturated chains in a partial order first considered by Richardson and Springer in their study of symmetric varieties.…
Defant, Engen, and Miller defined a permutation to be uniquely sorted if it has exactly one preimage under West's stack-sorting map. We enumerate classes of uniquely sorted permutations that avoid a pattern of length three and a pattern of…
We extend and generalize many of the enumerative results concerning West's stack-sorting map $s$. First, we prove a useful theorem that allows one to efficiently compute $|s^{-1}(\pi)|$ for any permutation $\pi$, answering a question of…
Starting from some considerations we make about the relations between certain difference statistics and the classical permutation statistics we study permutations whose inversion number and excedance difference coincide. It turns out that…
This paper makes a combinatorial study of the two monoids and the two types of tableaux that arise from the two possible generalizations of the Patience Sorting algorithm from permutations (or standard words) to words. For both types of…
We present a simple bijection between Baxter permutations of size $n$ and plane bipolar orientations with n edges. This bijection translates several classical parameters of permutations (number of ascents, right-to-left maxima,…
Given a permutation w, we show that the number of repeated letters in a reduced decomposition of w is always less than or equal to the number of 321- and 3412-patterns appearing in w. Moreover, we prove bijectively that the two quantities…
A permutation $\boldsymbol w$ gives rise to a graph $G_{\boldsymbol w}$; the vertices of $G_{\boldsymbol w}$ are the letters in the permutation and the edges of $G_{\boldsymbol w}$ are the inversions of $\boldsymbol w$. We find that the…
Based on the direct-sum-decomposition of the rth tensor power of the defining representation of the special orthogonal group SO(2k+1) one is interested in a bijective approach for determining the Frobenius characters of the isotypic…
Despite the fact that the field of pattern avoiding permutations has been skyrocketing over the last two decades, there are very few exhaustive generating algorithms for such classes of permutations. In this paper we introduce the notions…
A permutation is (1-23-4)-avoiding if it contains no four entries, increasing left to right, with the middle two adjacent in the permutation. Here we give a 2-variable recurrence for the number of such permutations, improving on the…