Related papers: A combinatorial model for the transition matrix be…

This paper is devoted to the presentation of a combinatorial approach for analyzing the performance of an important modulation protocol used in mobile telecommunications. We show in particular that a fundamental formula, in this context, is…

We define a partial order $\mathcal{P}_n$ on permutations of any given size $n$, which is the image of a natural partial order on inversion sequences. We call this the ``middle order''. We demonstrate that the poset $\mathcal{P}_n$ refines…

This article introduces an analogue of permutation classes in the context of polyominoes. For both permutation classes and polyomino classes, we present an original way of characterizing them by avoidance constraints (namely, with excluded…

We introduce k-crossings and k-nestings of permutations. We show that the crossing number and the nesting number of permutations have a symmetric joint distribution. As a corollary, the number of k-noncrossing permutations is equal to the…

We introduce inversions tableaux, a new combinatorial model for Schubert polynomials and Stanley symmetric functions that directly specializes to semi-standard Young tableaux in the Grassmannian case. They are a modification of the balanced…

In this article we consider square permutations, a natural subclass of permutations defined in terms of geometric conditions, that can also be described in terms of pattern avoiding permutations, and convex permutoninoes, a related subclass…

We propose a way of characterizing the algorithms computing a Walsh-Hadamard transform that consist of a sequence of arrays of butterflies ($I_{2^{n-1}}\otimes \text{DFT}_2$) interleaved by linear permutations. Linear permutations are those…

Networks can be combined in various ways, such as overlaying one on top of another or setting two side by side. We introduce "network models" to encode these ways of combining networks. Different network models describe different kinds of…

A permutohedral variety is a remarkable object in various areas of mathematics, and its topological invariants are widely recognized. However, only little is known about a real permutohedral variety, that is, the real locus of a…

A permutation may be represented by a collection of paths in the plane. We consider a natural class of such representations, which we call tangles, in which the paths consist of straight segments at 45 degree angles, and the permutation is…

In this article we explore some of the combinatorial consequences of recent results relating the isospectral commuting variety and the Hilbert scheme of points in the plane.

We establish a new simple explicit description of combinatorial wall-crossing for the rational Cherednik algebra applied to the trivial representation. In this way we recover a theorem of P. Dimakis and G. Yue. We also present two…

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…

Given a Stirling permutation w, we introduce the mesa set of w as the natural generalization of the pinnacle set of a permutation. Our main results characterize admissible mesa sets and give closed enumerative formulas in terms of rational…

We introduce a new rotation-invariant web basis for a family of Specht modules $S^{(d^3, 1^{n-3d})}$, indexed by normal plabic graphs satisfying a degree condition and resembling $A_2$ webs. We show that the $\mathfrak{S}_n$ action on our…

We begin a systematic study of the enumerative combinatorics of mixed succession rules, which are succession rules such that, in the associated generating tree, the nodes are allowed to produce their sons at several different levels…

Adaptive networks model social, physical, technical, or biological systems as attributed graphs evolving at the level of both their topology and data. They are naturally described by graph transformation, but the majority of authors take an…

Recently, there has been growing interest in the ability of Transformer-based models to produce meaningful embeddings of text with several applications, such as text similarity. Despite significant progress in the field, the explanations…

Recent work on permutation-based model merging has shown impressive low- or zero-barrier mode connectivity between models from completely different initializations. However, this line of work has not yet extended to the Transformer…

Transformer architectures show significant promise for natural language processing. Given that a single pretrained model can be fine-tuned to perform well on many different tasks, these networks appear to extract generally useful linguistic…