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

[31] Paths of homomorphisms from stable Kneser graphs
Carsten Schultz
Combinatorica, 2013, 33 : 613 - 621
[32] Counting paths in digraphs
Seymour, Paul
Sullivan, Blair D.
EUROPEAN JOURNAL OF COMBINATORICS, 2010, 31 (03) : 961 - 975
[33] Paths of homomorphisms from stable Kneser graphs
Schultz, Carsten
COMBINATORICA, 2013, 33 (05) : 613 - 621
[34] Counting Homomorphisms to Cactus Graphs Modulo 2
Gobel, Andreas
Goldberg, Leslie Ann
Richerby, David
31ST INTERNATIONAL SYMPOSIUM ON THEORETICAL ASPECTS OF COMPUTER SCIENCE (STACS 2014), 2014, 25 : 350 - 361
[35] Homomorphisms Are a Good Basis for Counting Small Subgraphs
Curticapean, Radu
Dell, Holger
Marx, Daniel
STOC'17: PROCEEDINGS OF THE 49TH ANNUAL ACM SIGACT SYMPOSIUM ON THEORY OF COMPUTING, 2017, : 210 - 223
[36] Counting homomorphisms onto finite solvable groups
Matei, D
Suciu, AI
JOURNAL OF ALGEBRA, 2005, 286 (01) : 161 - 186
[37] The complexity of counting graph homomorphisms (extended abstract)
Dyer, M
Greenhill, C
PROCEEDINGS OF THE ELEVENTH ANNUAL ACM-SIAM SYMPOSIUM ON DISCRETE ALGORITHMS, 2000, : 246 - 255
[38] A NOTE ON GENERALIZED DERIVATIONS AS A JORDAN HOMOMORPHISMS
Chandrasekhar, Arusha
Tiwari, Shailesh Kumar
BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 2020, 57 (03) : 709 - 737
[39] A note on homomorphisms between products of algebras
Chajda, Ivan
Goldstern, Martin
Langer, Helmut
ALGEBRA UNIVERSALIS, 2018, 79 (02)
[40] A note on Bockstein homomorphisms in local cohomology
Singh, Anurag K.
Walther, Uli
ARRANGEMENTS OF HYPERPLANES - SAPPORO 2009, 2012, 62 : 513 - +

← 1 2 3 4 5 →