combinatorics and commutative algebra second edition series editors hyman bass joseph oesterlé alan weinstein richard p. stanley combinatorics and commutative algebra second edition birkhäuser boston • basel • berlin library of congress cataloging-in-publication data stanley, richard p., 1944- combinatorics and commutative algebra / richard p. stanley. -- 2nd ed. p. cm. -- (progress in mathematics ; v. 41) includes bibliographical references. isbn 0-8176-3836-9 (alk. paper). -- isbn 3-7643-3836-9 (alk. paper) 1. commutative algebra. 2. combinatorial analysis. i. title. ii. series: progress in mathematics (boston, mass.) ; vol. 41 qa251.3.s72 1996 95-25196 512:24--dc20 cip printed on acid-free paper © 1996 birkhäuser boston, 2nd ed. 1983 birkhäuser boston, 1st ed. copyright is not claimed for works of u.s. government employees. all rights reserved. no part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without prior permission of the copyright owner. permission to photocopy for internal or personal use of specific clients is granted by birkhäuser boston for libraries and other users registered with the copyright clearance center (ccc), provided that the base fee of $6.00 per copy, plus $0.20 per page is paid directly to ccc, 222 rosewood drive, danvers, ma 01923, u.s.a. special requests should be addressed directly to birkhäuser boston, 675 massachusetts avenue, cambridge, ma 02139, u.s.a. isbn 0-8176-3836-9 isbn 3-7643-3836-9 layout, typesetting by texniques, boston, ma printed and bound by quinn-woodbine, woodbine, nj printed in the united states of america 9 8 7 6 5 4 3 2 1 contents preface to the second edition ..... vii preface to the first edition ..... viii notation ..... ix chapter 0: background 1. combinatorics .....combinatorics and commutative algebra second edition series editors hyman bass joseph oesterlé alan weinstein richard p. stanley combinatorics and commutative algebra second edition birkhäuser boston • basel • berlin library of congress cataloging-in-publication data stanley, richard p., 1944- combinatorics and commutative algebra / richard p. stanley. -- 2nd ed. p. cm. -- (progress in mathematics ; v. 41) includes bibliographical references. isbn 0-8176-3836-9 (alk. paper). -- isbn 3-7643-3836-9 (alk. paper) 1. commutative algebra. 2. combinatorial analysis. i. title. ii. series: progress in mathematics (boston, mass.) ; vol. 41 qa251.3.s72 1996 95-25196 512:24--dc20 cip printed on acid-free paper © 1996 birkhäuser boston, 2nd ed. 1983 birkhäuser boston, 1st ed. copyright is not claimed for works of u.s. government employees. all rights reserved. no part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without prior permission of the copyright owner. permission to photocopy for internal or personal use of specific clients is granted by birkhäuser boston for libraries and other users registered with the copyright clearance center (ccc), provided that the base fee of $6.00 per copy, plus $0.20 per page is paid directly to ccc, 222 rosewood drive, danvers, ma 01923, u.s.a. special requests should be addressed directly to birkhäuser boston, 675 massachusetts avenue, cambridge, ma 02139, u.s.a. isbn 0-8176-3836-9 isbn 3-7643-3836-9 layout, typesetting by texniques, boston, ma printed and bound by quinn-woodbine, woodbine, nj printed in the united states of america 9 8 7 6 5 4 3 2 1 contents preface to the second edition ..... vii preface to the first edition ..... viii notation ..... ix chapter 0: background 1. combinatorics .....