Results 91 to 100 of about 116,873 (193)

Bijections behind the Ramanujan Polynomials

Advances in Applied Mathematics, 2001
The Ramanujan polynomials were introduced by Ramanujan in his study of power series inversions. In an approach to the Cayley formula on the number of trees, Shor discovers a refined recurrence relation in terms of the number of improper edges, without realizing the connection to the Ramanujan polynomials.
Chen, William Y.C., Guo, Victor J.W.
openaire   +3 more sources

An extension of the cogrowth formula to arbitrary subsets of the tree

Bulletin of the London Mathematical Society, Volume 58, Issue 1, January 2026.
Abstract What is the probability that a random walk in the free group ends in a proper power? Or in a primitive element? We present a formula that computes the exponential decay rate of the probability that a random walk on a regular tree ends in a given subset, in terms of the exponential decay rate of the analogous probability of the non‐backtracking
Doron Puder
wiley   +1 more source

A simple explicit bijection between (n,2) Gog and Magog trapezoids

, 2015
A sub-problem of the open problem of finding an explicit bijection between alternating sign matrices and totally symmetric self-complementary plane partitions consists in finding an explicit bijection between so-called $(n,k)$ Gog trapezoids and $(n,k ...
Bettinelli, Jérémie
core   +1 more source

Producing New Bijections from Old

Advances in Mathematics, 1995
It is investigated when a bijection between finite sets \(A\), \(B\) can be constructed from a bijection between \(F(A)\) and \(F(B)\) for some \(F\). A very general category setting is exhibited and then applied to the cases of disjoint union, product, and power.
Feldman, D., Propp, J.
openaire   +1 more source

Module structure of Weyl algebras

Journal of the London Mathematical Society, Volume 113, Issue 1, January 2026.
Abstract The seminal paper (Stafford, J. Lond. Math. Soc. (2) 18 (1978), no. 3, 429–442) was a major step forward in our understanding of Weyl algebras. Beginning with Serre's Theorem on free summands of projective modules and Bass' Stable Range Theorem in commutative algebra, we attempt to trace the origins of this work and explain how it led to ...
Gwyn Bellamy
wiley   +1 more source

Block circulant graphs and the graphs of critical pairs of crowns

Electronic Journal of Graph Theory and Applications, 2019
In this paper, we provide a natural bijection between a special family of block circulant graphs and the graphs of critical pairs of the posets known as generalized crowns.
Rebecca E. Garcia, Pamela E. Harris, Bethany Kubik, Shannon Talbott   +3 more
doaj   +1 more source

Coxeter's enumeration of Coxeter groups

Journal of the London Mathematical Society, Volume 113, Issue 1, January 2026.
Abstract In a short paper that appeared in the Journal of the London Mathematical Society in 1934, H. S. M. Coxeter completed the classification of finite Coxeter groups. In this survey, we describe what Coxeter did in this paper and examine an assortment of topics that illustrate the broad and enduring influence of Coxeter's paper on developments in ...
Bernhard Mühlherr, Richard M. Weiss
wiley   +1 more source

Combinatorial Generation Algorithms for Directed Lattice Paths

Mathematics
Graphs are a powerful tool for solving various mathematical problems. One such task is the representation of discrete structures. Combinatorial generation methods make it possible to obtain algorithms that can create discrete structures with specified ...
Yuriy Shablya, Arsen Merinov, Dmitry Kruchinin   +2 more
doaj   +1 more source

Eulerian digraphs and Dyck words, a bijection

, 2014
The main goal of this work is to establish a bijection between Dyck words and a family of Eulerian digraphs. We do so by providing two algorithms implementing such bijection in both directions.
Codara, Pietro, D'Antona, Ottavio M., Genuzio, Marco   +2 more
core  

Bijective Recurrences concerning Schröder Paths [PDF]

The Electronic Journal of Combinatorics, 1998
Consider lattice paths in Z$^2$ with three step types: the up diagonal $(1,1)$, the down diagonal $(1,-1)$, and the double horizontal $(2,0)$. For $n \geq 1$, let $S_n$ denote the set of such paths running from $(0,0)$ to $(2n,0)$ and remaining strictly above the x-axis except initially and terminally.
openaire   +2 more sources