آمار
| تعداد نشریات | 5 |
| تعداد شماره‌ها | 108 |
| تعداد مقالات | 1,228 |
| تعداد مشاهده مقاله | 1,147,080 |
| تعداد دریافت فایل اصل مقاله | 1,006,004 |
A new construction for µ-way Steiner trades | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 13، دوره 9، شماره 2، شهریور 2024، صفحه 329-338 اصل مقاله (393.53 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2023.27862.1373 | ||
| نویسندگان | ||
| Saeedeh Rashidi* 1؛ Nasrin Soltankhah2 | ||
| 1Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran | ||
| 2Department of Mathematics, Faculty of mathematical Sciences, Alzahra University, Tehran, Iran | ||
| چکیده | ||
| A $\mu$-way $(v,k,t)$ trade $T$ of volume $m$ consists of $\mu$ pairwise disjoint collections $T_1, \ldots ,T_{\mu}$, each of $m$ blocks of size $k$ such that for every $t$-subset of a $v$-set $V,$ the number of blocks containing this $t$-subset is the same in each $T_i$ for $1\leq i\leq \mu$. If any $t$-subset of the $v$-set $V$ occurs at most once in each $T_i$ for $1\leq i\leq \mu$, then $T$ is called a $\mu$-way $(v,k,t)$ Steiner trade. In 2016, it was proved that there exists a 3-way $(v,k,2)$ Steiner trade of volume $m$ when $12(k-1)\leq m$ for each $k$. Here we improve the lower bound to $8(k-1)$ for even $k$, by using a recursive construction. | ||
| کلیدواژه‌ها | ||
| 3-way $(v, k, 2)$ Steiner trade؛ 1-solely balanced set؛ block design | ||
| مراجع | ||
|
[1] H. Amjadi and N. Soltankhah, The 3-way intersection problem for Kirkman triple systems, Graphs Combin. 33 (2017), no. 4, 673–687. https://doi.org/10.1007/s00373-017-1801-8 [2] H. Amjadi and N. Soltankhah, On the existence of d-homogeneous 3-way Steiner trades, Util. Math. 108 (2018), 307–320.
[3] M. Asgari and N. Soltankhah, On the non-existence of some Steiner $t − (v, k)$ trades of certain volumes, Util. Math. 79 (2009), 277–283.
[4] P. Chen and X. Wang, The 3-way intersection problem for kite systems, Graphs Combin. 34 (2018), no. 6, 1741–1749. https://doi.org/10.1007/s00373-018-1976-7 [5] S. Golalizadeh and N. Soltankhah, On the existence of $d$-homogeneous $mu$-way (v, 3, 2) Steiner trades, Graphs Combin. 35 (2019), 471–478. https://doi.org/10.1007/s00373-019-02008-3 [6] B.D. Gray and C. Ramsay, On a conjecture of Mahmoodian and Soltankhah regarding the existence of $(v, k, t)$ trades, Ars Combin. 48 (1998), 191–194.
[7] B.D. Gray and C. Ramsay, On the spectrum of Steiner $(v, k, t)$ trades (II), Graphs Combin. 15 (1999), no. 4, 405–415. https://doi.org/10.1007/s003730050074 [8] B.D. Gray and C. Ramsay, On the spectrum of Steiner $(v, k, t)$ trades I, J. Combin. Math. Combin. Comput. 34 (2000), 133–158.
[9] A.S. Hedayat, The theory of trade-off for t-designs, D. Ray-Chaudhuri: Coding Theory and Design Theory, Part II: Design Theory, , IMA Vol. Math. Appl., 1990, pp. 101–126.
[10] H.L. Hwang, On the structure of $(v, k, t)$ trades, J. Statist. Plann. Inference 13 (1986), 179–191.
[11] A. Khodkar and D.G. Hoffman, On the non-existence of Steiner $(v, k, 2)$ trades with certain volumes, Australas. J. Combin. 18 (1998), 303–312.
[12] D.S. Krotov, On the gaps of the spectrum of volumes of trades, J. Combin. Designs 26 (2018), no. 3, 119–126. https://doi.org/10.1002/jcd.21592 [13] C.C. Lindner and A. Rosa, Corrigendum:“Steiner triple systems having a prescribed number of triples in common”(Canad. J. Math. 27 (1975), no. 5, 1166–1175), Canad. J. Math. 30 (1978), no. 4, 896–896.
[14] E.S. Mahmoodian and N. Soltankhah, On the existence of $(v, k, t)$ trades., Australas. J. Combin. 6 (1992), 279–292.
[15] S. Milici and G. Quattrocchi, Some results on the maximum number of STSs such that any two of them intersect in the same block-set, J. Inform. Optim. Sci. 7 (1986), no. 3, 291–302. https://doi.org/10.1080/02522667.1986.10698862 [16] S. Rashidi and N. Soltankhah, On the possible volume of $mu-(v, k, t)$ trades, Bull. Iranian Math. Soc. 40 (2014), no. 6, 1387–1401.
[17] S. Rashidi and N. Soltankhah, On the 3-way $(v, k, 2)$ Steiner trades, Discrete Math. 339 (2016), no. 12, 2955–2963. https://doi.org/10.1016/j.disc.2016.06.006 [18] S. Rashidi and N. Soltankhah, A completion of the spectrum of 3-way $(v, k, 2)$ Steiner trades, Acta Appl. Math. 180 (2022), no. 1, Article number 4 https://doi.org/10.1007/s10440-022-00503-z [19] N. Soltankhah and H. Amjadi, The 3-way flower intersection problem for Steiner triple systems, Discrete Math. Theor. Comput. Sci. 22 (2020), 1–14. | ||
|
آمار تعداد مشاهده مقاله: 333 تعداد دریافت فایل اصل مقاله: 1,188 |
||