Application of Hadamard product to some combinatorial and probabilistic problems
Diskretnaya Matematika, Tome 28 (2016) no. 1, pp. 101-112 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

An improvement of the algebraic method of computing the Hadamard product of rational functions is given. Some applications of the Hadamard product to combinatorial and probabilistic problems are considered.
Mots-clés : Hadamard product
Keywords: generating functions, rational power series.
@article{DM_2016_28_1_a5,
     author = {E. A. Potekhina},
     title = {Application of {Hadamard} product to some combinatorial and probabilistic problems},
     journal = {Diskretnaya Matematika},
     pages = {101--112},
     year = {2016},
     volume = {28},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2016_28_1_a5/}
}
TY  - JOUR
AU  - E. A. Potekhina
TI  - Application of Hadamard product to some combinatorial and probabilistic problems
JO  - Diskretnaya Matematika
PY  - 2016
SP  - 101
EP  - 112
VL  - 28
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/DM_2016_28_1_a5/
LA  - ru
ID  - DM_2016_28_1_a5
ER  - 
%0 Journal Article
%A E. A. Potekhina
%T Application of Hadamard product to some combinatorial and probabilistic problems
%J Diskretnaya Matematika
%D 2016
%P 101-112
%V 28
%N 1
%U http://geodesic.mathdoc.fr/item/DM_2016_28_1_a5/
%G ru
%F DM_2016_28_1_a5
E. A. Potekhina. Application of Hadamard product to some combinatorial and probabilistic problems. Diskretnaya Matematika, Tome 28 (2016) no. 1, pp. 101-112. http://geodesic.mathdoc.fr/item/DM_2016_28_1_a5/

[1] Aizenberg L.A., Leinartas E.K., “Mnogomernaya kompozitsiya Adamara i yadra Sege”, Sibirskii matematicheskii zhurnal, 24:3 (1983), 3–10 | MR

[2] Elin M.M., “Mnogomernaya kompozitsiya Adamara”, Sibirskii matematicheskii zhurnal, 35:35 (1994), 1052–1057 | MR | Zbl

[3] Leinartas E.K., “Ob odnom obobschenii proizvedeniya Adamara v $C^{n}$”, Matematicheskie zametki, 32:4 (1982), 477–482 | MR

[4] De Loera J.A., Haws D., Hemmecke R., Yoshida R., “A computational study of integer programming algorithms based on Barvinok's rational functions”, Discrete Optimization, 2:2 (2005), 135–144 | DOI | MR | Zbl

[5] Bostan A., Boukraa S., Christol G., Hassani S., Maillard J-M., “Using $n$-fold integrals as diagonals of rational functions and integrality of series expansions”, J. Physics A: Math. and Theor., 46:18 (2013), 185201 | DOI | MR

[6] Zhilinskii B., “Generating functions for effective Hamiltonians via the symmetrized Hadamard product”, J. Physics A: Math. and Theor., 41:38 (2008), 382004 | DOI | MR | Zbl

[7] Stanley R., Enumerative Combinatorics, Wadsworth Brooks/Cole, 1984; Stenli R., Perechislitelnaya kombinatorika, Mir, Moskva, 1990, 440 pp. | MR

[8] Lando S.K., Lektsii o proizvodyaschikh funktsiyakh, MTsNMO, Moskva, 2007, 144 pp.

[9] Krivokolesko V.P., Leinartas E.K., “O tozhdestvakh s polinomialnymi koeffitsientami”, Izv. Irkutskogo gos. un-ta. Ser. Matem., 5:3 (2012), 56–62 | Zbl

[10] Rybnikov K.A., Kombinatornyi analiz. Ocherki istorii, Izd-vo mekh.-matem. f-ta MGU, Moskva, 1996, 125 pp.

[11] Han G.-N., “A general algorithm for the MacMahon omega operator”, Ann. Combinatorics, 7:4 (2003), 467–480 | DOI | MR | Zbl

[12] Potekhina E.A., Tolovikov M.I., “Raspredelenie serii v posledovatelnostyakh 1-zavisimykh indikatorov”, Cherepovetskie nauchnye chteniya - 2010: Mater. Vseros. nauch.-prakt. konf. Ch. 3: Tekhn., estestv. i ekon. nauki, 2011, 136–139, ChGU, Cherepovets

[13] Potekhina E.A., Tolovikov M.I., “Ostsilliruyuschee sluchainoe bluzhdanie i proizvedenie Adamara ratsionalnykh funktsii”, Diskretnaya matematika, 25:3 (2013), 96–115 ; Potekhina E. A., Tolovikov M. I., “Oscillating random walk and the Hadamard product of rational functions”, Discrete Math. Appl., 24:1 (2014), 29–44 | DOI | MR | DOI | Zbl

[14] Kim J.H., Hadamard products, lattice paths, and skew tableaux, PhD thesis, Brandeis Univ. Dep. Math. ProQuest, UMI Diss. Publ., 2013, 69 pp. | MR

[15] Feller W., An Introduction to Probability Theory and Its Applications, v. 1, 3rd edition, Wiley, 1968, 528 pp. ; Feller V., Vvedenie v teoriyu veroyatnostei i ee prilozheniya, V 2-kh tomakh. T. 1, Mir, Moskva, 1984, 528 pp. | MR | Zbl | MR

[16] Zhuk S.N., “Ob onlain-algoritmakh upakovki pryamougolnikov v neskolko polos”, Diskretnaya matematika, 19:4 (2007), 117–131 | DOI | MR | Zbl