Schur congruences, Carlitz sequences of polynomials and automaticity

被引：5
|
作者：
Allouche, JP
Skordev, G
机构：
[1] Univ Paris Sud, Ctr Orsay, CNRS, Rech Informat Lab,UMR 8623, F-91405 Orsay, France
[2] Univ Bremen, CEVIS, D-28359 Bremen, Germany
来源：
DISCRETE MATHEMATICS | 2000年 / 214卷 / 1-3期
关键词：
Schur congruence; Legendre and classical polynomials; automatic sequences;
D O I：
10.1016/S0012-365X(99)00195-8
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We first generalize the Schur congruence for Legendre polynomials to sequences of polynomials that we call 'd-Carlitz'. This notion is more general than a similar notion introduced by Carlitz. Then, we study automaticity properties of double sequences generated by these sequences of polynomials, thus generalizing previous results on the double sequences produced by one-dimensional linear cellular automata. (C) 2000 Elsevier Science B.V. All rights reserved.
引用
收藏
页码：21 / 49
页数：29
相关论文
共 50 条
  • [31] CARLITZ GENERALIZATIONS OF LUCAS AND LEHMER SEQUENCES
    SHANNON, AG
    MELHAM, RS
    FIBONACCI QUARTERLY, 1993, 31 (02): : 105 - 111
  • [32] CONGRUENCES CONCERNING LEGENDRE POLYNOMIALS
    Sun, Zhi-Hong
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2011, 139 (06) : 1915 - 1929
  • [33] EULERIAN POLYNOMIALS AND POLYNOMIAL CONGRUENCES
    Iijima, Kazuki
    Sasaki, Kyouhei
    Takahashi, Yuuki
    Yoshinaga, Masahiko
    CONTRIBUTIONS TO DISCRETE MATHEMATICS, 2019, 14 (01) : 46 - 54
  • [34] Congruences for Sheffer sequences
    Serafin, Grzegorz
    AUSTRALASIAN JOURNAL OF COMBINATORICS, 2024, 89 : 116 - 136
  • [35] Curious congruences for cyclotomic polynomials
    Akiyama, Shigeki
    Kaneko, Hajime
    RESEARCH IN NUMBER THEORY, 2022, 8 (04)
  • [36] The self-affine property of (U, r)-Carlitz sequences of polynomials deciphered in terms of graph directed IFS
    Ni, Tian-Jia
    Wen, Zhi-Ying
    DISCRETE APPLIED MATHEMATICS, 2009, 157 (18) : 3728 - 3742
  • [37] Schur polynomials and weighted Grassmannians
    Abe, Hiraku
    Matsumura, Tomoo
    JOURNAL OF ALGEBRAIC COMBINATORICS, 2015, 42 (03) : 875 - 892
  • [38] ON SEMIRING COMPLEXITY OF SCHUR POLYNOMIALS
    Fomin, Sergey
    Grigoriev, Dima
    Nogneng, Dorian
    Schost, Eric
    COMPUTATIONAL COMPLEXITY, 2018, 27 (04) : 595 - 616
  • [39] On semiring complexity of Schur polynomials
    Sergey Fomin
    Dima Grigoriev
    Dorian Nogneng
    Éric Schost
    computational complexity, 2018, 27 : 595 - 616
  • [40] Quantum multiplication of Schur polynomials
    Bertram, A
    Ciocan-Fontanine, I
    Fulton, W
    JOURNAL OF ALGEBRA, 1999, 219 (02) : 728 - 746
12345