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Hook Formulas for Skew Shapes IV. Increasing Tableaux and Factorial Grothendieck Polynomials
We present a new family of hook-length formulas for the number of standard increasing tableaux which arise in the study of factorial Grothendieck...
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Minuscule reverse plane partitions via quiver representations
A nilpotent endomorphism of a quiver representation induces a linear transformation on the vector space at each vertex. Generically among all...
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Experimenting with Standard Young Tableaux
Using symbolic computation with Maple, we can discover lots of (rigorously-proved!) facts about Standard Young Tableaux, in particular the...
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Cyclic quasi-symmetric functions
The ring of cyclic quasi-symmetric functions and its non-Escher subring are introduced in this paper. A natural basis consists of fundamental cyclic...
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Randomized Schützenberger’s Jeu De Taquin and Approximate Calculation of the Cotransition Probabilities of a Central Markov Process on the 3D Young Graph
There exists a well-known hook-length formula for calculating the dimensions of two-dimensional Young diagrams. Unfortunately, an analogous formula...
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Duality of Graded Graphs Through Operads
Pairs of graded graphs, together with the Fomin property of graded graph duality, are rich combinatorial structures providing among other a framework...
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An affine generalization of evacuation
We establish the existence of an involution on tabloids that is analogous to Schützenberger’s evacuation map on standard Young tableaux. We find that...
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Divided symmetrization and quasisymmetric functions
Motivated by a question in Schubert calculus, we study the interplay of quasisymmetric polynomials with the divided symmetrization operator, which...
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d-Complete Posets: Local Structural Axioms, Properties, and Equivalent Definitions
Although d -complete posets arose along the interface between algebraic combinatorics and Lie theory, they are defined using only requirements on...
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A Noncommutative Cycle Index and New Bases of Quasi-symmetric Functions and Noncommutative Symmetric Functions
We define a new basis of the algebra of quasi-symmetric functions by lifting the cycle-index polynomials of symmetric groups to noncommutative...
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A classification of spherical Schubert varieties in the Grassmannian
Let L be any standard Levi subgroup which acts by left multiplication on a Schubert variety X ( w ) in the Grassmannian. We give a complete...
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Positive Jantzen sum formulas for cyclotomic Hecke algebras
This paper proves a “positive” Jantzen sum formula for the Specht modules of the cyclotomic Hecke algebras of type A and uses it to obtain new bounds...
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Simultaneous core partitions with nontrivial common divisor
A tremendous amount of research has been done in the last two decades on ( s , t )-core partitions when s and t are relatively prime integers. Here we...
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Counting shellings of complete bipartite graphs and trees
A shelling of a graph, viewed as an abstract simplicial complex that is pure of dimension 1, is an ordering of its edges such that every edge is...
