PARTITION LATTICE Q-ANALOGS RELATED TO Q-STIRLING NUMBERS

被引：10

作者：

BENNETT, C

DEMPSEY, KJ

SAGAN, BE

机构：

[1] BOWLING GREEN STATE UNIV,DEPT MATH & STAT,BOWLING GREEN,OH 43403

[2] HILLSDALE COLL,DEPT MATH,HILLSDALE,MI 49242

[3] MICHIGAN STATE UNIV,DEPT MATH,E LANSING,MI 48824

来源：

JOURNAL OF ALGEBRAIC COMBINATORICS | 1994年 / 3卷 / 03期

关键词：

SET PARTITION LATTICE; VECTOR SPACE OVER A FINITE FIELD; Q-STIRLING NUMBER;

D O I：

10.1023/A:1022459817380

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We construct a family of partially ordered sets (posets) that are q-analogs of the set partition lattice. They are different from the q-analogs proposed by Dowling [5]. One of the important features of these posets is that their Whitney numbers of the first and second kind are just the q-Stirling numbers of the first and second kind, respectively. One member of this family [4] can be constructed using an interpretation of Milne [9] for S[n, k] as sequences of lines in a vector space over the Galois field F(q). Another member is constructed so as to mirror the partial order in the subspace lattice.

引用

页码：261 / 283

页数：23

共 13 条

[1]

Bjorner A., 1982, ORDERED SETS, P583

[2] Q-BERNOULLI NUMBERS AND POLYNOMIALS [J].