相关论文: A bijection for two sequences in OEIS

Let $G$ be a connected finite graph. Backman, Baker, and Yuen have constructed a family of explicit and easy-to-describe bijections $g_{\sigma,\sigma^*}$ between spanning trees of $G$ and $(\sigma,\sigma^*)$-compatible orientations, where…

Let $\Bigl\langle\matrix{n\cr k}\Bigr\rangle$, $\Bigl\langle\matrix{B_n\cr k}\Bigr\rangle$, and $\Bigl\langle\matrix{D_n\cr k}\Bigr\rangle$ be the Eulerian numbers in the types A, B, and D, respectively -- that is, the number of…

Inversion sequences of length $n$ are integer sequences $e_1,\ldots ,e_n$ with $0\le e_i<i$ for all $i$, which are in bijection with the permutations of length $n$. In this paper, we classify all Wilf equivalence classes of pattern-avoiding…

Combinatorial enumeration of various RNA secondary structures and protein contact maps, is of great interest for both combinatorists and computational biologists. Enumeration of protein contact maps has considerable difficulties due to the…

We show how a bijection due to Biane between involutions and labelled Motzkin paths yields bijections between Motzkin paths and two families of restricted involutions that are counted by Motzkin numbers, namely, involutions avoiding 4321…

For every finite Coxeter group W , we prove that the number of chains in the shard intersection lattice introduced by Reading on the one hand and in the BHZ poset introduced by Bergeron, Zabrocki and the third author on the other hand, are…

In this paper, we shall construct a bijection between rook placements on double staircases (introduced by Josuat-Verg\`es in 2017) and increasing binary trees. We introduce two subclasses of rook placements on double staircases, which we…

We present refined enumeration formulas for lattice paths in $\mathbb{Z}^2$ with two kinds of steps, by keeping track of the number of descents (i.e., turns in a given direction), the major index (i.e., the sum of the positions of the…

A $B$-tree is a type of search tree where every node (except possibly for the root) contains between $m$ and $2m$ keys for some positive integer $m$, and all leaves have the same distance to the root. We study sequences of $B$-trees that…

Present article deals with trajectorial intersections in linear fractional systems ('systems'). We propose a classification of intersections of trajectories in three classes viz. trajectories intersecting at same time(EIST), trajectories…

A bijection is constructed between two sets of height restricted lattice paths by means of translating them in two tree classe, namely plane trees and Elena trees. An old bijection between them can be used now for that actual problem.

Link prediction plays an important role in understanding intrinsic evolving mechanisms of networks. With the belief that the likelihood of the existence of a link between two nodes is strongly related with their similarity, many methods…

For the OEIS sequence A002627, defined by the inhomogeneous first-order recurrence $a(n) = n\,a(n-1) + 1$ with $a(0) = 0$, R.~J.~Mathar recorded in February 2014 the conjectured second-order homogeneous recurrence \[ a(n) - (n+1)\,a(n-1) +…

We study the combinatorics of the change of basis of three representations of the stationary state algebra of the two parameter simple asymmetric exclusion process. Each of the representations considered correspond to a different set of…

We show that any multiplicative bijection between the algebras of differentiable functions, defined on differentiable manifolds of positive dimension, is an algebra isomorphism, given by composition with a unique diffeomorphism.

Using a direct algebraic approach we derive convolution identities for second order sequences, hereby distinguishing between sequences obeying the same or different recurrence relations. We also state a general convolution for Horadam…

We establish a general bijective framework for encoding faces of some classical hyperplane arrangements. Precisely, we consider hyperplane arrangements in $\mathbb{R}^n$ whose hyperplanes are all of the form $\{x_i-x_j=s\}$ for some…

Let $A_k$ be the set of permutations in the symmetric group $S_k$ with prefix 12. This paper concerns the enumeration of involutions which avoid the set of patterns $A_k$. We present a bijection between symmetric Schroder paths of length…

In this expository article we collect the integer sequences that count several different types of matrices over finite fields and provide references to the Online Encyclopedia of Integer Sequences (OEIS). Section 1 contains the sequences,…

We extend so-called slit-slide-sew bijections to constellations and quasiconstellations. We present an involution on the set of hypermaps given with an orientation, one distinguished corner, and one distinguished edge leading away from the…