We consider the problem of elastic matching of sequences of real numbers. Since both a query and a target sequence may be noisy, i.e., contain some outlier elements, it is desirable to exclude the outlier elements from matching in order to obtain a robust matching performance. Moreover, in many applications like shape alignment or stereo correspondence it is also desirable to have a one-to-one and onto correspondence (bijection) between the remaining elements. We propose an algorithm that determines the optimal subsequence bijection (OSB) of a query and target sequence. The OSB is efficiently computed since we map the problem's solution to a cheapest path in a DAG (directed acyclic graph). We obtained excellent results on standard benchmark time series datasets. We compared OSB to Dynamic Time Warping (DTW) with and without warping window. We do not claim that OSB is always superior to DTW. However, our results demonstrate that skipping outlier elements as done by OSB can significantly improve matching results for many real datasets. Moreover, OSB is particularly suitable for partial matching. We applied it to the object recognition problem when only parts of contours are given. We obtained sequences representing shapes by representing object contours as sequences of curvatures.

Cited by 46

Le principe de bijection

Hilda Koopman, Dominique Sportiche · Communications · 1984

Koopman Hilda, Sportiche Dominique. Le principe de bijection. In: Communications, 40, 1984. Grammaire générative et sémantique, sous la direction de Pierre Jacob. pp. 135-147.

Cited by 3

A Rogers-Ramanujan bijection

Adriano M. Garsia, Stephen C. Milne · Journal of Combinatorial Theory Series A · 1981

Cited by 114

On Sundaram's full bijection

Jacinta Torres · arXiv (Cornell University) · 2017

We highlight refinement of a bijection given by Sheila Sundaram in her PhD thesis. The framework allows for comparison to a late conjecture of Naito-Sagaki. We give an injection of the set of dominant paths for this model into the corresponding set of Littlewood-Richardson Sundaram tableaux, which is not surjective. We relate this to the refinement of the aforementioned bijection.

Cited by 0Open access

Morsel 37. An Unexpected Bijection

Ross Honsberger · American Mathematical Society eBooks · 1991

Cited by 0

Han’s bijection via permutation codes

William Y. C. Chen, Neil J. Y. Fan, Teresa X. S. Li · European Journal of Combinatorics · 2010

Cited by 2

The active bijection for graphs

Emeric Gioan, Michel Las Vergnas · Advances in Applied Mathematics · 2019

Cited by 7Open access

Han's Bijection via Permutation Codes

William Y. C. Chen, Neil J. Y. Fan, Teresa X. S. Li · arXiv (Cornell University) · 2010

We show that Han's bijection when restricted to permutations can be carried out in terms of the cyclic major code and the cyclic inversion code. In other words, it maps a permutation $π$ with a cyclic major code $(s_1, s_2, ..., s_n)$ to a permutation $σ$ with a cyclic inversion code $(s_1,s_2, ..., s_n)$. We also show that the fixed points of Han's map can be characterized by the strong fixed points of Foata's second fundamental transformation. The notion of strong fixed points is related to partial Foata maps introduced by Björner and Wachs.

Cited by 0Open access

A bijection for ordered factorizations

Richard Garfield, Donald E. Knuth, Herbert S. Wilf · Journal of Combinatorial Theory Series A · 1990

Cited by 3

A Bijection for Enriched Trees

William Y. C. Chen · European Journal of Combinatorics · 1994

Cited by 0

A McKay bijection for projectors

Gabriel Navarro · Revista Matemática Iberoamericana · 2021

If \mathfrak F is a saturated formation of groups, we define a canonical subset \text{Irr}_{\mathfrak F'}(G) of the irreducible complex characters of a finite solvable group G . If H is an \mathfrak F -projector of G , we show that |\text{Irr}_{\mathfrak F'}(G)|=|\text{Irr}(\mathbf{N}_G(H)/H')| , where H'=[H,H] is the derived subgroup of H . In particular, if \mathfrak F is the class of p -groups, this reproves the solvable case of the celebrated McKay conjecture.

Cited by 3Open access

A bijection for rooted maps . . .

Guillaume Chapuy, Michel Marcus, Gilles Schaeffer · 2012

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 Vauquelin in the eighties, we describe a bijection between rooted maps, or rooted bipartite quadrangulations, on a surface of genus g and some simpler objects that generalize plane trees. Thanks to a rerooting argument, our bijection allows to compute the generating series of rooted maps on a surface of genus g with respect to the number of edges, and to recover the asymptotic numbers of such maps. Our construction allows to keep track in a bipartite quadrangulation of the distances of all vertices to a random basepoint. This is an analog for higher genus surfaces of the basic result on which were built the recent advances in the comprehension of the intrinsec geometry of large random planar maps, hopefully opening the way to the study of a model of continuum random surfaces of genus g.

Cited by 0

The active bijection for graphs

Emeric Gioan, Michel Las Vergnas · arXiv (Cornell University) · 2018

The active bijection forms a package of results studied by the authors in a series of papers in oriented matroids. The present paper is intended to state the main results in the particular case, and more widespread language, of graphs. We associate any directed graph, defined on a linearly ordered set of edges, with one particular of its spanning trees, which we call its active spanning tree. For any graph on a linearly ordered set of edges, this yields a surjective mapping from orientations onto spanning trees, which preserves activities (for orientations in the sense of Las Vergnas, for spanning trees in the sense of Tutte), as well as some partitions (or filtrations) of the edge set associated with orientations and spanning trees. It yields a canonical bijection between classes of orientations and spanning trees, as well as a refined bijection between all orientations and edge subsets, containing various noticeable bijections [...]. Several constructions of independent interest are involved. The basic case concerns bipolar orientations, which are in bijection with their fully optimal spanning trees, as proved in a previous paper, and as computed in a companion paper. We give a canonical decomposition of a directed graph on a linearly ordered set of edges into acyclic/cyclic bipolar directed graphs. Considering all orientations of a graph, we obtain an expression of the Tutte polynomial in terms of products of beta invariants of minors, a remarkable partition of the set of orientations into activity classes, and a simple expression of the Tutte polynomial using four orientation activity parameters. We derive a similar decomposition theorem for spanning trees. We also provide a general deletion/contraction framework for these bijections and relatives.

Cited by 3Open access

Lenart's Bijection via Bumpless Pipe Dreams

Adam Gregory, Zachary Hamaker · The Electronic Journal of Combinatorics · 2023

Pipe dreams and bumpless pipe dreams for vexillary permutations are each known to be in bijection with certain semistandard tableaux via maps due to Lenart and Weigandt, respectively. Recently, Gao and Huang have defined a bijection between the former two sets. In this note we show for vexillary permutations that the Gao-Huang bijection preserves the associated tableaux, giving a new proof of Lenart's result. Our methods extend to give a recording tableau for any bumpless pipe dream.

Cited by 0Open access