Partial geometric designs having circulant concurrence matrices

We classify small partial geometric designs (PGDs) by spectral characteristics of their concurrence matrices. It is well known that the concurrence matrix of a PGD can have at most three distinct eigenvalues, all of which are nonnegative integers. The matrix contains useful information on the incide...

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Published in:	Journal of combinatorial designs Vol. 30; no. 6; pp. 420 - 460
Main Authors:	Song, Sung‐Yell, Tranel, Theodore
Format:	Journal Article
Language:	English
Published:	Hoboken Wiley Subscription Services, Inc 01.06.2022
Subjects:	1 1 2 $1\frac{1}{2}$‐design association scheme Combinatorial analysis Eigenvalues Mathematical analysis Matrices (mathematics) partial geometric difference set partial geometry special partially balanced incomplete block design strongly regular graph t $t$‐design
ISSN:	1063-8539, 1520-6610
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Abstract	We classify small partial geometric designs (PGDs) by spectral characteristics of their concurrence matrices. It is well known that the concurrence matrix of a PGD can have at most three distinct eigenvalues, all of which are nonnegative integers. The matrix contains useful information on the incidence structure of the design. An ordinary 2‐ ( v , k , λ ) $(v,k,\lambda )$ design has a single concurrence λ $\lambda $, and its concurrence matrix is circulant, a partial geometry has two concurrences 1 and 0, and a transversal design TD λ ( k , u ) ${\text{TD}}_{\lambda }(k,u)$ has two concurrences λ $\lambda $ and 0, and its concurrence matrix is circulant. In this paper, we survey the known PGDs by highlighting their concurrences and constructions. Then we investigate which symmetric circulant matrices are realized as the concurrence matrices of PGDs. In particular, we try to give a list of all PGDs of order up to 12 each of which has a circulant concurrence matrix. We then describe these designs along with their combinatorial properties and constructions. This work is part of the second author's Ph.D. dissertation [46].
AbstractList	We classify small partial geometric designs (PGDs) by spectral characteristics of their concurrence matrices. It is well known that the concurrence matrix of a PGD can have at most three distinct eigenvalues, all of which are nonnegative integers. The matrix contains useful information on the incidence structure of the design. An ordinary 2‐(v,k,λ) $(v,k,\lambda )$ design has a single concurrence λ $\lambda $, and its concurrence matrix is circulant, a partial geometry has two concurrences 1 and 0, and a transversal design TDλ(k,u) ${\text{TD}}_{\lambda }(k,u)$ has two concurrences λ $\lambda $ and 0, and its concurrence matrix is circulant. In this paper, we survey the known PGDs by highlighting their concurrences and constructions. Then we investigate which symmetric circulant matrices are realized as the concurrence matrices of PGDs. In particular, we try to give a list of all PGDs of order up to 12 each of which has a circulant concurrence matrix. We then describe these designs along with their combinatorial properties and constructions. This work is part of the second author's Ph.D. dissertation [46]. We classify small partial geometric designs (PGDs) by spectral characteristics of their concurrence matrices. It is well known that the concurrence matrix of a PGD can have at most three distinct eigenvalues, all of which are nonnegative integers. The matrix contains useful information on the incidence structure of the design. An ordinary 2‐ ( v , k , λ ) $(v,k,\lambda )$ design has a single concurrence λ $\lambda $, and its concurrence matrix is circulant, a partial geometry has two concurrences 1 and 0, and a transversal design TD λ ( k , u ) ${\text{TD}}_{\lambda }(k,u)$ has two concurrences λ $\lambda $ and 0, and its concurrence matrix is circulant. In this paper, we survey the known PGDs by highlighting their concurrences and constructions. Then we investigate which symmetric circulant matrices are realized as the concurrence matrices of PGDs. In particular, we try to give a list of all PGDs of order up to 12 each of which has a circulant concurrence matrix. We then describe these designs along with their combinatorial properties and constructions. This work is part of the second author's Ph.D. dissertation [46]. We classify small partial geometric designs (PGDs) by spectral characteristics of their concurrence matrices. It is well known that the concurrence matrix of a PGD can have at most three distinct eigenvalues, all of which are nonnegative integers. The matrix contains useful information on the incidence structure of the design. An ordinary 2‐ design has a single concurrence , and its concurrence matrix is circulant, a partial geometry has two concurrences 1 and 0, and a transversal design has two concurrences and 0, and its concurrence matrix is circulant. In this paper, we survey the known PGDs by highlighting their concurrences and constructions. Then we investigate which symmetric circulant matrices are realized as the concurrence matrices of PGDs. In particular, we try to give a list of all PGDs of order up to 12 each of which has a circulant concurrence matrix. We then describe these designs along with their combinatorial properties and constructions. This work is part of the second author's Ph.D. dissertation [46].
Author	Tranel, Theodore Song, Sung‐Yell
Author_xml	– sequence: 1 givenname: Sung‐Yell orcidid: 0000-0002-6404-5430 surname: Song fullname: Song, Sung‐Yell email: sysong@iastate.edu organization: Iowa State University – sequence: 2 givenname: Theodore surname: Tranel fullname: Tranel, Theodore organization: Iowa State University
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References	1997; 80 1980; 28 2018; 341 1974; 55 1938; 43 1960; 31 2005; 396 2013; 22 1978; 55 2021; 29 2017; 24 1968; 103 1976 2017; 293 1953; 6 1991 1974; 9 1997; 3 1966; 10 2012; 33 2018; 86 1979 1999 1963; 13 1942; 6 1952; 23 1952; 47 1976; 14 2001 2019; 87 1988; 47 2017; 33 1970; 22 1984 2016; 80 2014; 30 1953; 24 1976; 16 1976; 15 2016; 24 1989 2016; 45 e_1_2_8_29_1 e_1_2_8_24_1 e_1_2_8_47_1 e_1_2_8_25_1 e_1_2_8_46_1 e_1_2_8_26_1 e_1_2_8_49_1 e_1_2_8_48_1 Brouwer A. E. (e_1_2_8_13_1) 1984 e_1_2_8_3_1 e_1_2_8_2_1 Cameron P. J. (e_1_2_8_16_1) 2017; 293 Bose R. C. (e_1_2_8_4_1) 1942; 6 e_1_2_8_5_1 e_1_2_8_7_1 e_1_2_8_6_1 e_1_2_8_9_1 e_1_2_8_8_1 e_1_2_8_20_1 e_1_2_8_43_1 e_1_2_8_21_1 e_1_2_8_42_1 e_1_2_8_22_1 e_1_2_8_45_1 e_1_2_8_23_1 e_1_2_8_44_1 e_1_2_8_41_1 Feng R. (e_1_2_8_28_1) 2016; 45 e_1_2_8_40_1 e_1_2_8_17_1 Hanani H. (e_1_2_8_32_1) 1974 e_1_2_8_18_1 e_1_2_8_39_1 e_1_2_8_19_1 e_1_2_8_36_1 e_1_2_8_14_1 e_1_2_8_35_1 e_1_2_8_15_1 e_1_2_8_38_1 e_1_2_8_37_1 e_1_2_8_10_1 e_1_2_8_31_1 e_1_2_8_11_1 e_1_2_8_34_1 e_1_2_8_12_1 Elliot J. E. H. (e_1_2_8_27_1) 1966; 10 e_1_2_8_33_1 e_1_2_8_30_1
References_xml	– volume: 80 start-page: 13 issue: 1 year: 1997 end-page: 78 article-title: A unifying construction for difference sets publication-title: J. Combin. Theory Ser. A – volume: 9 start-page: 1 year: 1974 end-page: 18 article-title: Special partially balanced incomplete block designs and associated graphs publication-title: Discrete Math. – volume: 103 start-page: 239 year: 1968 end-page: 258 article-title: Planes of order n with collineation groups of order publication-title: Math. Z – volume: 14 start-page: 251 year: 1976 end-page: 269 article-title: Affine resolvable balanced incomplete block designs: a survey publication-title: Aequantiones Math. – start-page: 85 year: 1984 end-page: 122 – volume: 23 start-page: 367 year: 1952 end-page: 383 article-title: Combinatorial properties of group divisible designs publication-title: Ann. Math. Stat. – year: 2001 – year: 1989 – volume: 6 start-page: 1 year: 1942 end-page: 15 article-title: An affine analogue of Singer's theorem publication-title: J. Indian Math. Soc. – volume: 24 start-page: 381 issue: 3 year: 2017 end-page: 392 article-title: Constructions of ‐designs from unitary geometry over finite fields publication-title: Algebra Colloq. – volume: 80 start-page: 435 issue: 3 year: 2016 end-page: 451 article-title: Partial geometric designs with prescribed automorphisms publication-title: Des. Codes Cryptogr. – volume: 13 start-page: 389 year: 1963 end-page: 419 article-title: Strongly regular graphs, partial geometries, and partially balanced designs publication-title: Pacific J. Math. – volume: 16 start-page: 1 year: 1976 end-page: 7 article-title: A characterization of partial geometric designs publication-title: Discrete Math. – volume: 87 start-page: 2655 issue: 11 year: 2019 end-page: 2670 article-title: Partial geometric designs from group actions publication-title: Des. Codes Cryptogr – year: 1979 – volume: 22 start-page: 252 issue: 6 year: 2013 end-page: 269 article-title: Symmetric ‐designs and ‐difference sets publication-title: J. Combin. Des – volume: 24 start-page: 112 issue: 3 year: 2016 end-page: 131 article-title: Partial geometric difference families publication-title: J. Combin. Des – volume: 6 start-page: 35 year: 1953 end-page: 41 article-title: An embedding theorem for balanced incomplete block designs publication-title: Canad. J. Math. – volume: 24 start-page: 167 year: 1953 end-page: 195 article-title: On the construction of group divisible incomplete block designs publication-title: Ann. Math. Stat. – volume: 47 start-page: 151 year: 1952 end-page: 184 article-title: Classification and analysis of partially balanced incomplete block designs with two associate classes publication-title: J. Amer. Statist. Assoc. – year: 1984 – volume: 293 start-page: 111 issue: 1 year: 2017 end-page: 126 article-title: Research problems from the 19th British combinatorial conference publication-title: Discrete Math. – volume: 28 start-page: 226 year: 1980 end-page: 248 article-title: ‐designs publication-title: J. Combin. Theory Ser. A – start-page: 49 year: 1976 end-page: 81 – volume: 45 start-page: 817 issue: 6 year: 2016 end-page: 839 article-title: Directed strongly regular graphs and their constructions publication-title: Adv. Math. (China) – volume: 10 start-page: 517 year: 1966 end-page: 531 article-title: Relative difference sets publication-title: Illinois J. Math. – volume: 396 start-page: 303 year: 2005 end-page: 316 article-title: Combinatorial designs with two singular values II. Partial geometric designs publication-title: Linear Algebra Appl. – volume: 31 start-page: 789 year: 1960 end-page: 791 article-title: On the block structure of certain P.B.I.B. designs with triangular and association schemes publication-title: Ann. Math. Statist. – volume: 33 start-page: 591 issue: 5 year: 2017 end-page: 606 article-title: New partial geometric difference sets and partial geometric difference families publication-title: Acta Math. Sin. (Engl. Ser.) – volume: 33 start-page: 1174 issue: 6 year: 2012 end-page: 1177 article-title: Directed strongly regular graphs from ‐designs publication-title: European J. Combin. – volume: 29 start-page: 271 issue: 5 year: 2021 end-page: 306 article-title: Partial geometric designs with block sizes three and four publication-title: J. Combin. Des. – volume: 22 start-page: 597 year: 1970 end-page: 614 article-title: Strongly regular graphs derived from combinatorial designs publication-title: Canad. J. Math. – volume: 86 start-page: 1367 issue: 6 year: 2018 end-page: 1375 article-title: A framework for constructing partial geometric difference sets publication-title: Des. Codes Cryptogr. – volume: 55 start-page: 42 year: 1974 end-page: 52 – volume: 341 start-page: 2490 issue: 9 year: 2018 end-page: 2498 article-title: Partial geometric difference sets and partial geometric difference families publication-title: Discrete Math. – volume: 55 start-page: 257 year: 1978 end-page: 280 article-title: Strongly regular graphs with strongly regular subconstituents publication-title: J. Algebra. – year: 1991 – volume: 3 start-page: 234 year: 1997 end-page: 256 article-title: On the existence of abelian Hadamard difference sets and a new family of difference sets publication-title: Finite Fields Appl. – volume: 47 start-page: 71 issue: 1 year: 1988 end-page: 100 article-title: A directed graph version of strongly regular graphs publication-title: J. Combin. Theory Ser. A – volume: 15 start-page: 263 issue: 3 year: 1976 end-page: 296 article-title: ‐Designs on hypergraphs publication-title: Discrete Math. – volume: 43 start-page: 377 year: 1938 end-page: 385 article-title: A theorem in projective geometry and some applications to number theory publication-title: Trans. Amer. Math. Soc. – volume: 24 start-page: 533 issue: 12 year: 2016 end-page: 552 article-title: A family of partial geometric designs from three‐class association schemes publication-title: J. Combin. Des – year: 1999 – volume: 30 start-page: 1529 year: 2014 end-page: 1549 article-title: Some families of directed strongly regular graphs obtained from certain finite incidence structures publication-title: Graphs Combin. – start-page: 42 volume-title: Combinatorics year: 1974 ident: e_1_2_8_32_1 – ident: e_1_2_8_48_1 – ident: e_1_2_8_47_1 doi: 10.1090/S0002-9947-1938-1501951-4 – ident: e_1_2_8_14_1 doi: 10.1007/978-3-642-74341-2 – ident: e_1_2_8_22_1 doi: 10.1006/jcta.1997.2796 – ident: e_1_2_8_30_1 doi: 10.4153/CJM-1970-067-9 – ident: e_1_2_8_31_1 doi: 10.4153/CJM-1954-005-4 – ident: e_1_2_8_35_1 doi: 10.1007/s10114-016-6151-6 – volume: 6 start-page: 1 year: 1942 ident: e_1_2_8_4_1 article-title: An affine analogue of Singer's theorem publication-title: J. Indian Math. Soc. – ident: e_1_2_8_9_1 doi: 10.1214/aoms/1177729027 – volume: 45 start-page: 817 issue: 6 year: 2016 ident: e_1_2_8_28_1 article-title: Directed strongly regular graphs and their constructions publication-title: Adv. Math. (China) – ident: e_1_2_8_20_1 doi: 10.1006/ffta.1997.0184 – ident: e_1_2_8_40_1 doi: 10.1002/jcd.21416 – ident: e_1_2_8_38_1 doi: 10.1007/s10623-015-0111-5 – ident: e_1_2_8_10_1 doi: 10.1016/0012-365X(76)90088-1 – ident: e_1_2_8_6_1 doi: 10.1080/01621459.1952.10501161 – ident: e_1_2_8_23_1 doi: 10.1007/s10623-017-0400-2 – ident: e_1_2_8_33_1 doi: 10.1016/0012-365X(76)90030-3 – ident: e_1_2_8_36_1 doi: 10.1007/s10623-019-00644-7 – ident: e_1_2_8_26_1 doi: 10.1016/0097-3165(88)90043-X – ident: e_1_2_8_43_1 doi: 10.1002/jcd.21354 – ident: e_1_2_8_2_1 – ident: e_1_2_8_21_1 doi: 10.1016/j.laa.2004.09.015 – ident: e_1_2_8_39_1 doi: 10.1002/jcd.21518 – ident: e_1_2_8_18_1 doi: 10.1016/0021-8693(78)90220-X – start-page: 85 volume-title: Enumeration and Design year: 1984 ident: e_1_2_8_13_1 – ident: e_1_2_8_24_1 – ident: e_1_2_8_7_1 doi: 10.1214/aoms/1177729382 – ident: e_1_2_8_11_1 doi: 10.1016/0012-365X(74)90068-5 – ident: e_1_2_8_49_1 doi: 10.1017/CBO9780511987045 – ident: e_1_2_8_15_1 doi: 10.1016/j.ejc.2012.01.011 – ident: e_1_2_8_25_1 doi: 10.1007/BF01111042 – ident: e_1_2_8_17_1 doi: 10.1017/CBO9780511623714 – ident: e_1_2_8_41_1 – ident: e_1_2_8_3_1 doi: 10.1017/CBO9780511549533 – ident: e_1_2_8_37_1 doi: 10.1016/0097-3165(80)90067-9 – ident: e_1_2_8_19_1 doi: 10.1016/j.disc.2018.06.008 – ident: e_1_2_8_8_1 – ident: e_1_2_8_44_1 doi: 10.1007/s00373-013-1364-2 – ident: e_1_2_8_45_1 doi: 10.1214/aoms/1177705806 – ident: e_1_2_8_29_1 doi: 10.1142/S1005386717000232 – ident: e_1_2_8_5_1 doi: 10.2140/pjm.1963.13.389 – ident: e_1_2_8_12_1 – volume: 10 start-page: 517 year: 1966 ident: e_1_2_8_27_1 article-title: Relative difference sets publication-title: Illinois J. Math. – volume: 293 start-page: 111 issue: 1 year: 2017 ident: e_1_2_8_16_1 article-title: Research problems from the 19th British combinatorial conference publication-title: Discrete Math. – ident: e_1_2_8_46_1 doi: 10.1007/BF01835977 – ident: e_1_2_8_42_1 – ident: e_1_2_8_34_1 doi: 10.1002/jcd.21767
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Snippet	We classify small partial geometric designs (PGDs) by spectral characteristics of their concurrence matrices. It is well known that the concurrence matrix of a...
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SubjectTerms	1 1 2 $1\frac{1}{2}$‐design association scheme Combinatorial analysis Eigenvalues Mathematical analysis Matrices (mathematics) partial geometric difference set partial geometry special partially balanced incomplete block design strongly regular graph t $t$‐design
Title	Partial geometric designs having circulant concurrence matrices
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