Related papers: Inserting rim-hooks into reverse plane partitions
The generating function of reverse plane partitions of a fixed shape factors into a product featuring the hook-lengths of this shape. This result, which was first obtained by Stanley, can be explained bijectively using the Hillman-Grassl…
R. Sulzgruber's rim hook insertion and the Hillman-Grassl correspondence are two distinct bijections between the reverse plane partitions of a fixed partition shape and multisets of rim-hooks of the same partition shape. It is known that…
The Hillman--Grassl correspondence is a well-known bijection between multisets of rim hooks of a partition shape $\lambda$ and reverse plane partitions of $\lambda$. We use the tools of quiver representations to generalize Hillman--Grassl…
The classical Robinson--Schensted--Knuth correspondence is a bijection from nonnegative integer matrices to pairs of semi-standard Young tableaux. Based on the work of, among others, Burge, Hillman, Grassl, Knuth and Gansner, it is known…
We generalize the Robinson-Schensted-Knuth algorithm to the insertion of two row arrays of multisets. This generalization leads to new enumerative results that have representation theoretic interpretations as decompositions of centralizer…
We study the coupling of pairs of reverse plane partitions of the same shape by assigning a certain local interaction between the reverse plane partitions. We show that they are in bijection with a certain Yang-Baxter integrable colored…
The enumeration of maps and the study of uniform random maps have been classical topics of combinatorics and statistical physics ever since the seminal work of Tutte in the sixties. Following the bijective approach initiated by Cori and…
Cylindric plane partitions may be thought of as a natural generalization of reverse plane partitions. A generating series for the enumeration of cylindric plane partitions was recently given by Borodin. As in the reverse plane partition…
Some conjectures on partition hook lengths, recently stated by the author, have been proved and generalized by Stanley, who also needed a formula by Andrews, Goulden and Jackson on symmetric functions to complete his derivation. Another…
Recently, there has been a lot of work on combinatorial inequalities related to hook-lengths in $t$-regular partitions. In this short note, we give a proof using generating functions for a result proved by Singh and Barman (2026) using…
In this short note, we will give a generalization of the indefinite Schwarz-Pick inequality due to Seto [8]. Our approach is based on a connection between complex geometry and the geometry of reproducing kernel Hilbert spaces, which was…
In this note a bijection is constructed between the set of partitions of n simultaneously s-regular and t-distinct, and those simultaneously t-regular and s-distinct. Some implications of the map are discussed. As a generalized version of…
We study some combinatorial properties of higher-dimensional partitions which generalize plane partitions. We present a natural bijection between $d$-dimensional partitions and $d$-dimensional arrays of nonnegative integers. This bijection…
We unify and extend previous bijections on plane quadrangulations to bipartite and quasibipartite plane maps. Starting from a bipartite plane map with a distinguished edge and two distinguished corners (in the same face or in two different…
Super RSK correspondence is a bijective correspondence between superbiwords and pairs of semistandard supertableaux. Such a bijection was given by Bonetti, Senato and Venezia, via an insertion algorithm closely related to Schensted…
A bijection is defined from Littlewood-Richardson tableaux to rigged configurations. It is shown that this map preserves the appropriate statistics, thereby proving a quasi-particle expression for the generalized Kostka polynomials, which…
Another bijective proof of Stanley's hook-content formula for the generating function for semistandard tableaux of a given shape is given that does not involve the involution principle of Garsia and Milne. It is the result of a merge of the…
Suppose the rows of a board are partitioned into sets of m rows called levels. An m-level rook placement is a subset of the board where no two squares are in the same column or the same level. We construct explicit bijections to prove three…
We define a birational map between labelings of a rectangular poset and its associated trapezoidal poset. This map tropicalizes to a bijection between the plane partitions of these posets of fixed height, giving a new bijective proof of a…
The paper presents a proof of the Hodge Riemann relations for the combinatorial intersection cohomology of a polytope, as fist given by K.Karu, in terms of geometric operations on polytopes.