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The generalized Oberwolfach problem asks for a factorization of the complete graph $K_v$ into prescribed $2$-factors and at most a $1$-factor. When all $2$-factors are pairwise isomorphic and $v$ is odd, we have the classic Oberwolfach problem, which
Externí odkaz:
http://arxiv.org/abs/2307.11246
Autor:
Fallat, Shaun, Joshi, Neha, Maleki, Roghayeh, Meagher, Karen, Mojallal, Seyed Ahmad, Nasserasr, Shahla, Shirazi, Mahsa N., Razafimahatratra, Andriaherimanana Sarobidy, Stevens, Brett
Zero forcing is a combinatorial game played on a graph with the ultimate goal of changing the colour of all the vertices at minimal cost. Originally this game was conceived as a one player game, but later a two-player version was devised in-conjuncti
Externí odkaz:
http://arxiv.org/abs/2306.01138
Autor:
Hoyt, Adam, Stevens, Brett
Publikováno v:
J. Combin. Math. Combin. Comput. 107 (2018) 149-170
A complementary Gray code for binary n-tuples is one that, when all the tuples are complemented, is identical to itself; this is equivalent to the complement of the first half of the code being identical to the second half. We generalize the notion o
Externí odkaz:
http://arxiv.org/abs/2210.14301
Autor:
Colbourn, Charles J., Ingalls, Colin, Jedwab, Jonathan, Saaltink, Mark, Smith, Ken W., Stevens, Brett
A pair of planes, both projective or both affine, of the same order and on the same pointset are orthogoval if each line of one plane intersects each line of the other plane in at most two points. In this paper we prove new constructions for sets of
Externí odkaz:
http://arxiv.org/abs/2210.11961
Autor:
Chafee, Amanda Lynn, Stevens, Brett
A \textbf{double change covering design} is a $v$-set $X$ and an ordered list $\mathcal{L}$ of $b$ blocks of size $k$ where every $t$-set must occur in at least one block. Each pair of consecutive blocks differs by exactly two elements. A double chan
Externí odkaz:
http://arxiv.org/abs/2209.12275
Autor:
Chafee, Amanda, Stevens, Brett
A \textbf{single change covering design} is a $v$-set $X$ and an ordered list $\cL$ of $b$ blocks of size $k$ where every $t$-set must occur in at least one block. Each pair of consecutive blocks differs by exactly one element. A single change coveri
Externí odkaz:
http://arxiv.org/abs/2209.11010
Autor:
Castoldi, André Guerino, Carmelo, Emerson L. Monte, Moura, Lucia, Panario, Daniel, Stevens, Brett
This work shows several direct and recursive constructions of ordered covering arrays using projection, fusion, column augmentation, derivation, concatenation and cartesian product. Upper bounds on covering codes in NRT spaces are also obtained by im
Externí odkaz:
http://arxiv.org/abs/2208.01410
Autor:
Castoldi, André Guerino, Carmelo, Emerson Luiz do Monte, Moura, Lucia, Panario, Daniel, Stevens, Brett
Publikováno v:
CAI 2019. Lecture Notes in Computer Science, vol 11545. Springer
In this work, constructions of ordered covering arrays are discussed and applied to obtain new upper bounds on covering codes in Rosenbloom-Tsfasman spaces (RT spaces), improving or extending some previous results.
Comment: 12 pages
Comment: 12 pages
Externí odkaz:
http://arxiv.org/abs/2208.01412
Publikováno v:
IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 63, NO. 2, FEBRUARY 2017
We present a new construction of ordered orthogonal arrays (OOA) of strength $t$ with $(q + 1)t$ columns over a finite field $\mathbb{F}_{q}$ using linear feedback shift register sequences (LFSRs). OOAs are naturally related to $(t, m, s)$-nets, line
Externí odkaz:
http://arxiv.org/abs/2208.00333