# Báo cáo toán học: "Counting subwords in a partition of a set"

## Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Department of Mathematic dành cho các bạn yêu thích môn toán học đề tài: Counting subwords in a partition of a set. | Counting subwords in a partition of a set Toufik Mansour Department of Mathematics University of Haifa 31905 Haifa Israel toufik@ Mark Shattuck Department of Mathematics University of Tennessee Knoxville TN 37996 shattuck@ Sherry . Yan Department of Mathematics Zhejiang Normal University 321004 Jinhua . China huifangyan@ Submitted Sep 22 2009 Accepted Jan 15 2010 Published Jan 22 2010 Mathematics Subject Classification 05A18 05A15 05A05 68R05 Abstract A partition n of the set n 1 2 . n is a collection B1 . Bk of nonempty disjoint subsets of n called blocks whose union equals n . In this paper we find explicit formulas for the generating functions for the number of partitions of n containing exactly k blocks where k is fixed according to the number of occurrences of a subword pattern T for several classes of patterns including all words of length 3. In addition we find simple explicit formulas for the total number of occurrences of the patterns in question within all the partitions of n containing k blocks providing both algebraic and combinatorial proofs. 1 Introduction A partition of n 1 2 . n is a decomposition of n into non-overlapping subsets B1 B2 . Bk called blocks which are listed in increasing order of their least elements 1 k n . We will represent a partition n B1 B2 . Bk in the canonical sequential form n n1n2 nn such that j G Bn. 1 j n. Therefore a sequence n n1n2 nn over the alphabet k represents a partition of n with k blocks if and only if it is a restricted growth function of n onto k see . 11 13 14 for details . For instance The third author was supported by the National Natural Science Foundation of China no. 10901141 . THE ELECTRONIC JOURNAL OF COMBINATORICS 17 2010 R19 1 123214154 is the canonical sequential form of the partition 1 5 7 2 4 3 6 9 8 of 9 . Throughout this paper partitions will be identified with their corresponding canonical sequences. The set of all partitions of n with exactly k .

TÀI LIỆU LIÊN QUAN
32    57    0
45    42    0
6    65    0
4    53    0
6    55    0
6    52    0
6    45    0
5    59    0
7    58    0
6    64    0
TÀI LIỆU XEM NHIỀU
13    32510    1652
3    19378    204
25    18683    3691
20    16774    1477
16    15868    2497
14    14343    2540
37    13059    2802
1    11365    401
3    10980    212
23    10568    384
TỪ KHÓA LIÊN QUAN
TÀI LIỆU MỚI ĐĂNG
9    17    1    07-07-2022
13    18    1    07-07-2022
6    9    1    07-07-2022
24    23    1    07-07-2022
10    13    1    07-07-2022
101    1    1    07-07-2022
11    3    1    07-07-2022
400    12    1    07-07-2022
40    13    1    07-07-2022
8    106    3    07-07-2022
35    11    1    07-07-2022
22    2    1    07-07-2022
19    15    1    07-07-2022
241    17    1    07-07-2022
18    10    1    07-07-2022
95    2    1    07-07-2022
6    21    1    07-07-2022
12    57    1    07-07-2022
9    35    2    07-07-2022
34    28    2    07-07-2022
TÀI LIỆU HOT
3    19378    204
13    32510    1652
3    1509    75
580    3634    346
62    4389    1
584    1964    81
171    3993    621
2    1751    72
51    2480    150
53    3346    175
Đã phát hiện trình chặn quảng cáo AdBlock
Trang web này phụ thuộc vào doanh thu từ số lần hiển thị quảng cáo để tồn tại. Vui lòng tắt trình chặn quảng cáo của bạn hoặc tạm dừng tính năng chặn quảng cáo cho trang web này.