A Note on Counting Homomorphisms of Paths

被引：1

作者：

Eggleton, Roger B. ^{[1
]}

Morayne, Michal ^{[2
]}

机构：

[1] Illinois State Univ, Dept Math, Normal, IL 61790 USA

[2] Wroclaw Univ Technol, Inst Math & Comp Sci, PL-50370 Wroclaw, Poland

来源：

GRAPHS AND COMBINATORICS | 2014年 / 30卷 / 01期

关键词：

Path; Homomorphism; Generating function; Catalan number; Endomorphism; ALGORITHM; NUMBER;

D O I：

10.1007/s00373-012-1261-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We obtain two identities and an explicit formula for the number of homomorphisms of a finite path into a finite path. For the number of endomorphisms of a finite path these give over-count and under-count identities yielding the closed-form formulae of Myers. We also derive finite Laurent series as generating functions which count homomorphisms of a finite path into any path, finite or infinite.

引用

页码：159 / 170

页数：12

共 50 条

[21] Counting Homomorphisms to Trees Modulo a Prime
Goebel, Andreas
Lagodzinski, J. A. Gregor
Seidel, Karen
ACM TRANSACTIONS ON COMPUTATION THEORY, 2021, 13 (03)
[22] Parameterized Counting of Partially Injective Homomorphisms
Roth, Marc
ALGORITHMICA, 2021, 83 (06) : 1829 - 1860
[23] THE COMPLEXITY OF COUNTING SURJECTIVE HOMOMORPHISMS AND COMPACTIONS
Focke, Jacob
Goldberg, Leslie Ann
Zivny, Stanislav
SIAM JOURNAL ON DISCRETE MATHEMATICS, 2019, 33 (02) : 1006 - 1043
[24] On counting homomorphisms to directed acyclic graphs
Dyer, Martin
Goldberg, Leslie Ann
Paterson, Mike
JOURNAL OF THE ACM, 2007, 54 (06)
[25] A note on the representation of lattice homomorphisms
Victoria A. Tamaeva
Batradz B. Tasoev
Positivity, 2024, 28 (5)
[26] A note on homomorphisms of Kneser hypergraphs
Bonomo-Braberman, Flavia
Dourado, Mitre C.
Valencia-Pabon, Mario
Vera, Juan C.
APPLIED MATHEMATICS AND COMPUTATION, 2020, 366
[27] A NOTE ON HOMOMORPHISMS OF OPERATOR ALGEBRAS
PORTA, H
COLLOQUIUM MATHEMATICUM, 1969, 20 (01) : 117 - &
[28] A note on homomorphisms of matrix semigroup
Omladic, Matjaz
Kuzma, Bojan
ARS MATHEMATICA CONTEMPORANEA, 2013, 6 (02) : 247 - 252
[29] A note on continuous behavior homomorphisms
Fuhrmann, PA
SYSTEMS & CONTROL LETTERS, 2003, 49 (05) : 359 - 363
[30] Counting paths in digraphs
Seymour, Paul
Sullivan, Blair D.
EUROPEAN JOURNAL OF COMBINATORICS, 2010, 31 (03) : 961 - 975

← 1 2 3 4 5 →