## Combinatorics AdvancesCharles J. Colbourn, Ebdollah Sayed Mahmoodian On March 28~31, 1994 (Farvardin 8~11, 1373 by Iranian calendar), the Twenty fifth Annual Iranian Mathematics Conference (AIMC25) was held at Sharif University of Technology in Tehran, Islamic Republic of Iran. Its sponsors in~ eluded the Iranian Mathematical Society, and the Department of Mathematical Sciences at Sharif University of Technology. Among the keynote speakers were Professor Dr. Andreas Dress and Professor Richard K. Guy. Their plenary lec~ tures on combinatorial themes were complemented by invited and contributed lectures in a Combinatorics Session. This book is a collection of refereed papers, submitted primarily by the participants after the conference. The topics covered are diverse, spanning a wide range of combinatorics and al~ lied areas in discrete mathematics. Perhaps the strength and variety of the pa~ pers here serve as the best indications that combinatorics is advancing quickly, and that the Iranian mathematics community contains very active contributors. We hope that you find the papers mathematically stimulating, and look forward to a long and productive growth of combinatorial mathematics in Iran. |

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### Contents

II | 1 |

IV | 2 |

V | 3 |

VI | 4 |

VII | 6 |

VIII | 8 |

IX | 11 |

X | 13 |

LXVI | 148 |

LXIX | 149 |

LXX | 150 |

LXXII | 152 |

LXXIII | 153 |

LXXV | 161 |

LXXVI | 181 |

LXXVII | 182 |

XI | 14 |

XII | 15 |

XIII | 16 |

XV | 17 |

XVI | 18 |

XVII | 19 |

XVIII | 21 |

XIX | 22 |

XX | 27 |

XXI | 29 |

XXII | 32 |

XXIII | 35 |

XXIV | 44 |

XXV | 45 |

XXVI | 49 |

XXVIII | 50 |

XXIX | 52 |

XXX | 61 |

XXXI | 65 |

XXXII | 77 |

XXXIII | 79 |

XXXIV | 81 |

XXXV | 87 |

XXXVI | 91 |

XXXVII | 92 |

XXXVIII | 94 |

XXXIX | 97 |

XL | 100 |

XLI | 102 |

XLII | 111 |

XLIII | 121 |

XLIV | 123 |

XLV | 127 |

XLVI | 129 |

XLIX | 131 |

LI | 132 |

LIII | 134 |

LV | 135 |

LVII | 136 |

LVIII | 138 |

LIX | 139 |

LX | 140 |

LXI | 141 |

LXII | 142 |

LXIII | 143 |

LXV | 145 |

LXXVIII | 189 |

LXXIX | 202 |

LXXX | 207 |

LXXXI | 210 |

LXXXII | 217 |

LXXXIII | 218 |

LXXXIV | 225 |

LXXXV | 226 |

LXXXVI | 228 |

LXXXVII | 235 |

LXXXVIII | 236 |

LXXXIX | 237 |

XC | 238 |

XCI | 240 |

XCII | 243 |

XCIV | 246 |

XCV | 247 |

XCVI | 251 |

XCVII | 252 |

XCVIII | 253 |

XCIX | 255 |

C | 257 |

CI | 258 |

CII | 259 |

CIII | 261 |

CIV | 267 |

CVI | 268 |

CVIII | 270 |

CIX | 271 |

CX | 274 |

CXI | 277 |

CXIII | 279 |

CXIV | 281 |

CXV | 287 |

CXVI | 293 |

CXVII | 294 |

CXVIII | 296 |

CXIX | 298 |

CXX | 299 |

CXXI | 307 |

CXXII | 310 |

CXXIII | 312 |

CXXIV | 315 |

CXXV | 321 |

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1995 Kluwer Academic 2)-rotational 9 mod algebraic algorithm applied Arpanet automorphism base triples beans Beatty sequences blocks Boolean functions C. J. Colbourn Colbourn and E. S. column Combinatorics Combinatorics Advances complete complete graph conjecture consider construction contains Corollary cut-complex cutset cycles decomposition denoted digraph Discrete Math disjoint dual E. S. Mahmoodian eds edge elements exists finite geometry graph G Graph Theory Hadamard Hadamard matrices Hamiltonian heap hyperplane ISBN isomorphic Kluwer Academic Publishers Lemma linear programming lower bounds matrix minimal MOLS mutually orthogonal latin nim-value NSM(G obtained orthogonal latin squares pair Permutation plane player polynomial polytopes positive integer problem Proof quadratic residues satisfying sequence space sequences simple Skolem squares of side Steiner triple systems STS(v subgraph subset subsquares symbols Tehran Theorem 3.1 tilings total chromatic total graphs transversal designs triples of Type two-terminal vectors vertex vertices

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