Related papers: Partial Alternating Sign Matrix Bijections and Dyn…

We present a simple bijection between permutation matrices and descending plane partitions without special parts. This bijection is already mentioned in work of P. Lalonde (without giving the details); it involves the inversion words of…

We are interested in finding an explicit bijection between two families of combinatorial objects: Gog and Magog triangles. These two families are particular classes of Gelfand-Tsetlin triangles and are respectively in bijection with…

A cornerstone of geometric reconstruction, rotation averaging seeks the set of absolute rotations that optimally explains a set of measured relative orientations between them. In addition to being an integral part of bundle adjustment and…

We present determinant formulae for the number of tilings of various domains in relation with Alternating Sign Matrix and Fully Packed Loop enumeration.

In this paper, we extend the recently introduced concept of partially dual ribbon graphs to graphs. We then go on to characterize partial duality of graphs in terms of bijections between edge sets of corresponding graphs. This result…

Alternating sign matrices (ASMs) are square matrices with entries 0, 1, or -1 whose rows and columns sum to 1 and whose nonzero entries alternate in sign. We present a unifying perspective on ASMs and other combinatorial objects by studying…

We give a bijection between partially directed paths in the symmetric wedge y= +/-x and matchings, which sends north steps to nestings. This gives a bijective proof of a result of Prellberg et al. that was first discovered through the…

We study the enumeration of diagonally and antidiagonally symmetric alternating sign matrices (DASASMs) of fixed odd order by introducing a case of the six-vertex model whose configurations are in bijection with such matrices. The model…

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 present novel equivalences in random matrix and tensor models between complex and self-adjoint theories with nontrivial quadratic terms in the action, established through an intermediate field representation. More precisely, we show that…

We survey structures endowed with natural partial orderings and prove their universality. These partial orders include partial orders on sets of words, partial orders formed by geometric objects, grammars, polynomials and homomorphism order…

Many models for chaotic systems consist of joining two integrable systems with incompatible constants of motion. The quantum counterparts of such models have a propagator which factorizes into two integrable parts. Each part can be…

A new combinatorial object is introduced, the part-frequency matrix sequence of a partition, which is elementary to describe and is naturally motivated by Glaisher's bijection. We prove results that suggest surprising usefulness for such a…

We introduce a new combinatorial object called tower diagrams and prove fundamental properties of these objects. We also introduce an algorithm that allows us to slide words to tower diagrams. We show that the algorithm is well-defined only…

As shown by A. Melnikov, the orbits of a Borel subgroup acting by conjugation on upper-triangular matrices with square zero are indexed by involutions in the symmetric group. The inclusion relation among the orbit closures defines a partial…

We exhibit a bijection between recently-introduced combinatorial objects known as valid hook configurations and certain weighted set partitions. When restricting our attention to set partitions that are matchings, we obtain three new…

For a subclass of matchings, set partitions, and permutations, we describe a direct bijection involving only arc annotated diagrams that not only interchanges maximum nesting and crossing numbers, but also all refinements of crossing and…

Half turn symmetric alternating sign matrices (HTSASMs) are special variations of the well-known alternating sign matrices which have a long and fascinating history. HTSASMs are interesting combinatorial objects in their own right and have…

We elucidate a bijection between ribbon graphs on the real projective plane and non-crossing annular pairings that relate to the $1/N$ correction term of the GOE and LOE spectral moments. We also derive analogous objects for the $1/N^2$…

In a recent paper, Ayyer and Behrend present for a wide class of partitions factorizations of Schur polynomials with an even number of variables where half of the variables are the reciprocals of the others into symplectic and/or orthogonal…