On the congruences of some combinatorial numbers

Sen Peng Eu, Shu Chung Liu, Yeong Nan Yeh

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

In this paper, we apply Lucas' theorem to evaluate the congruences of several combinatorial numbers, including the central Delannoy numbers and a class of Apéry-like numbers, the numbers of noncrossing connected graphs, the numbers of total edges of all noncrossing connected graphs on n vertices, etc. One of these results verifies a conjecture given by Deutsch and Sagan recently. In the end, we use an automaton to explain the idea of our approach.

Original languageEnglish
Pages (from-to)135-144
Number of pages10
JournalStudies in Applied Mathematics
Volume116
Issue number2
DOIs
Publication statusPublished - 2006 Feb 1

Fingerprint

Congruence
Connected graph
Automata
Verify
Evaluate
Theorem

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

On the congruences of some combinatorial numbers. / Eu, Sen Peng; Liu, Shu Chung; Yeh, Yeong Nan.

In: Studies in Applied Mathematics, Vol. 116, No. 2, 01.02.2006, p. 135-144.

Research output: Contribution to journalArticle

Eu, Sen Peng ; Liu, Shu Chung ; Yeh, Yeong Nan. / On the congruences of some combinatorial numbers. In: Studies in Applied Mathematics. 2006 ; Vol. 116, No. 2. pp. 135-144.
@article{5eaf9ad23d5b40519e1f2e5677d31f81,
title = "On the congruences of some combinatorial numbers",
abstract = "In this paper, we apply Lucas' theorem to evaluate the congruences of several combinatorial numbers, including the central Delannoy numbers and a class of Ap{\'e}ry-like numbers, the numbers of noncrossing connected graphs, the numbers of total edges of all noncrossing connected graphs on n vertices, etc. One of these results verifies a conjecture given by Deutsch and Sagan recently. In the end, we use an automaton to explain the idea of our approach.",
author = "Eu, {Sen Peng} and Liu, {Shu Chung} and Yeh, {Yeong Nan}",
year = "2006",
month = "2",
day = "1",
doi = "10.1111/j.1467-9590.2006.00337.x",
language = "English",
volume = "116",
pages = "135--144",
journal = "Studies in Applied Mathematics",
issn = "0022-2526",
publisher = "Wiley-Blackwell",
number = "2",

}

TY - JOUR

T1 - On the congruences of some combinatorial numbers

AU - Eu, Sen Peng

AU - Liu, Shu Chung

AU - Yeh, Yeong Nan

PY - 2006/2/1

Y1 - 2006/2/1

N2 - In this paper, we apply Lucas' theorem to evaluate the congruences of several combinatorial numbers, including the central Delannoy numbers and a class of Apéry-like numbers, the numbers of noncrossing connected graphs, the numbers of total edges of all noncrossing connected graphs on n vertices, etc. One of these results verifies a conjecture given by Deutsch and Sagan recently. In the end, we use an automaton to explain the idea of our approach.

AB - In this paper, we apply Lucas' theorem to evaluate the congruences of several combinatorial numbers, including the central Delannoy numbers and a class of Apéry-like numbers, the numbers of noncrossing connected graphs, the numbers of total edges of all noncrossing connected graphs on n vertices, etc. One of these results verifies a conjecture given by Deutsch and Sagan recently. In the end, we use an automaton to explain the idea of our approach.

UR - http://www.scopus.com/inward/record.url?scp=33645051965&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33645051965&partnerID=8YFLogxK

U2 - 10.1111/j.1467-9590.2006.00337.x

DO - 10.1111/j.1467-9590.2006.00337.x

M3 - Article

AN - SCOPUS:33645051965

VL - 116

SP - 135

EP - 144

JO - Studies in Applied Mathematics

JF - Studies in Applied Mathematics

SN - 0022-2526

IS - 2

ER -